publications (incl. preprints)
2018:
- Klingenberg, Markfelder, S.: “Non-uniqueness of energy-conservative solutions to the isentropic compressible two-dimensional Euler equations ”, Journal of Hyperbolic Differential Equations, Vol. 15,4 (2018) view PDF
- Klingenberg, Pirner, M., Puppo, G. : “Kinetic ES-BGK models for a multi-component gas mixture”, published in C. Klingenberg and M. Westdickenberg (eds.), Theory, Numerics and Applications of Hyperbolic Problems, Springer Proceedings in Mathematics & Statistics (PROMS) 236 (2018)view PDF
- Klingenberg, C., Li, Q., Pirner, M. : “On quantifying uncertainties for the BGK kinetic equation”, published in C. Klingenberg and M. Westdickenberg (eds.), Theory, Numerics and Applications of Hyperbolic Problems, Springer Proceedings in Mathematics & Statistics (PROMS) 236 (2018) view PDF
- Chandrashekar, P., Gallego, P., Klingenberg, C., : “A Runge-Kutta discontinuous Galerkin scheme for the ideal Magnetohydrodynamical model”, published in C. Klingenberg and M. Westdickenberg (eds.), Theory, Numerics and Applications of Hyperbolic Problems, Springer Proceedings in Mathematics & Statistics (PROMS) 236 (2018) view PDF
- Colombo, R., Klingenberg, C., Meltzer, M. : “A multispecies traffic model based on the Lighthill Whitham model”, published in C. Klingenberg and M. Westdickenberg (eds.), Theory, Numerics and Applications of Hyperbolic Problems, Springer Proceedings in Mathematics & Statistics (PROMS) 236 (2018) view PDF
- Klingenberg, C., Klotzky, J., Seguin, N.: “On well-posedness for a multi-particle-fluid model”, published in C. Klingenberg and M. Westdickenberg (eds.), Theory, Numerics and Applications of Hyperbolic Problems, Springer Proceedings in Mathematics & Statistics (PROMS) 236 (2018) view PDF
- Klingenberg, C., Thomann, A.: “On computing compressible Euler equations with gravity”, published in C. Klingenberg and M. Westdickenberg (eds.), Theory, Numerics and Applications of Hyperbolic Problems, Springer Proceedings in Mathematics & Statistics (PROMS) 236 (2018) view PDF
- Klingenberg, C., Schnücke, G., Xia, Y.: “An arbitrary Lagrangian-Eulerian discontinuous Galerkin method for conservation laws: Entropy stability”, published in C. Klingenberg and M. Westdickenberg (eds.), Theory, Numerics and Applications of Hyperbolic Problems, Springer Proceedings in Mathematics & Statistics (PROMS) 236 (2018) view PDF
- Berberich, J., Chandrashekar, P., Klingenberg, C.: “A general well-balanced finite volume scheme for Euler equations with gravity”, published in C. Klingenberg and M. Westdickenberg (eds.), Theory, Numerics and Applications of Hyperbolic Problems, Springer Proceedings in Mathematics & Statistics (PROMS) 236 (2018) view PDF
- J. Badwaik, M. Boileau, D. Coulette, E. Franck, P. Helluy, C. Klingenberg, L. Mendoza, H. Oberlin, “Task-based parallelization of an implicit kinetic scheme”, ESAIM: Proceedings and Surveys, vol. 63, June (2018) view PDF
- Roy, S, Annunziato, M., Borzi, M. Klingenberg, C.: “A Fokker-Planck approach to control collective motion”, Computational Optimization and Applications, Vol. 69, (2018) view PDF
- Xie, Feng & Klingenberg, C.: “A limit problem for three dimensional ideal compressible radiation magneto-hydrodynamics” Analysis and Applications, vol. 16, 1, pp. 85 - 102, (2018)
- Klingenberg, C. & Pirner, M.: “Existence, Uniqueness and Positivity of solutions for BGK models for mixtures”, Journal of Differential Equations, 264, pp. 207-227 (2018) view PDF
- Markfelder, S., Klingenberg, C. : “The Riemann problem for the multidimensional isentropic system of gas dynamics is ill-posed if it contains a shock”, Volume 227, 3, Archve for Rational Mechanics and Analysis (2018) view PDF
2017:
- Barsukow, W., Edelmann, P., Klingenberg, C., Röpke, F.: “A low-Mach Roe-type solver for the Euler equations allowing for gravity source terms”, ESAIM: Proceedings and Surveys, vol. 58, (2017) view PDF
- Klingenberg, C.: “Numerical Methods for Astrophysics”, Handbook of Numerical Analysis Vol. XVIII, edited by Abgrall & Shu, North Holland (2017) view PDF
- Barsukow, W., Edelmann, P., Klingenberg, C., Miczek, F, Röpke, F.: “A numerical scheme for the compressible low-Mach number regime of ideal fluid dynamics”, Journal of Scientific Computing, Volume 72, Issue 2, pp. 623–646, (2017) view PDF
- Klingenberg, C., Pirner, M., Puppo, G.: “A consistent kinetic model for a two component mixture with an application to plasma”, Kinetic and Related Models Vol. 10, No. 2, pp. 445–465 (2017), view PDF
- Klingenberg, C., Schnücke, G.., Xia, Y.: "Arbitrary Lagrangian-Eulerian discontinuous Galerkin method for conservation laws: analysis and application in one dimension”, Mathematics of Computations, Vol. 86, pp. 1203-1232, (2017) view PDF
- Klingenberg, C., Schnücke, G.., Xia, Y.: “An Arbitrary Lagrangian-Eulerian local discontinuous Galerkin method for Hamilton- Jacobi equations” Journal of Scientific Computating, Vol. 73, pp. 906-942 (2017) view PDF
- Klingenberg, C., Pörner, F., Xia, Y.: “An efficient implementation of the divergence free constraint in a discontinuous Galerkin method for magnetohydrodynamics on unstructured meshes”, Communication in Computational Physics, Vol. 21, No. 2, pp. 423-442, (2017) view PDF
2016:
- Touma, R., Koley, U., Klingenberg, C.: “Well-balanced unstaggered central schemes for the Euler equation with gravity”, SIAM J. Sci. Comp. 38, no. 5, pp. B773–B807, (2016) view PDF
- Sastoque, E., Klingenberg, C., Rendon, L., Juajibioy, J.: 2016: “Regularity of viscous solutions for a degenerate non-linear Cauchy problem”, J. Part. Diff. Eq., Vol. 29, No. 1, pp. 14-21 (2016), , view PDF
- Bauer, A., Schaal, K., Springel, V., Chandrashekar, P., Pakmor, R. and Klingenberg, C.: “Simulating turbulence using the discontinuous Galerkin code TENET”, Lecture Notes in Computational Science and Engineering (LNCSE), Springer Verlag (2016)) view PDF
- Gallego-Valencia, P., Klingenberg, C., Chandrashekar, Praveen: “On limiting for higher order discontinuous Galerkin methods for 2D Euler equations”, Bulletin of the Brazilian Math. Society, New Series, March 2016, Volume 47, Issue 1, pp. 335-345 (2016) view PDF
- Lu, Yun-guang; Lu, Xue-zhou; Klingenberg, C.; “The Cauchy problem for Multiphase First-Contact Miscible Models with Viscous Fingering”, Nonlinear Analysis, Real World Applications, Volume 27, February 2016, Pages 43–54 view PDF
- Desveaux, V. Zenk, M. Berthon, B. and Klingenberg, C.; 2016: Well-balanced schemes to capture non-explicit steady states on the Euler equation with a gravity, “International Journal for Numerical Methods in Fluids”, Volume 81, Issue 2, pp. 104–127, (2016) view PDF
- Desveaux, V., Zenk, M., Berthon, C., Klingenberg, C.: Well balanced schemes to capture non-explicit steady states: Ripa model, Mathematics of Computation, Volume 85, Number 300, July 2016 view PDF
- Chandrashekar, Praveen; Klingenberg, Christian: “Entropy stable finite volume scheme for ideal compressible MHD on 2-d cartesian meshes”, SIAM Journal on Numerical Analysis, Vol. 54, No. 2, pp. 1313–1340 (2016) view PDF
2015:
- Schaal, K., Bauer, A., Chandrashekar, Praveen, Pakmor, R., Klingenberg,C., Springel, V.: “Astrophysical hydrodynamics with a high-order discontinuous Galerkin scheme and adaptive mesh refinement”, Monthly Notices Royal Astronomical Society, Volume 453, Issue 4, Pages 4278–4300 (2015) view PDF
- Touma, R., Klingenberg, C.: “Well-balanced central finite volume methods for the Ripa system”, Applied Numerical Mathematics, 97 (2015) view PDF
- Chandrashekar, Praveen; Klingenberg, Christian; 2015: “A second order well-balanced finite volume method for the Euler equations with a gravity”, SIAM Journal on Scientific Computing, 37(3), B382–B402. (21 pages) (2015) view PDF
- Klingenberg, C., Koley, U., Lu, Y, Lu, X.: 2015: Decay rate of degenerate convection diffusion equations in both one and several Space dimensions, Acta Mathematica Scientia, 35B(2) view PDF
2014:
- Gallego, J., Löbbert, J, Bastian, P., Müthing, S., Klingenberg, C., Xia, Y.: Implementating a discontinuous Galerkin method for the compressible, inviscid Euler equations in the DUNE framework, Proceedings in Applied Mathematics and Mechanics, Vol. 14,1 (2014) view PDF
- Lu, Y., Klingenberg, C., Rendon, L., Sheng, De-Yin: Global solutions for a simplified shallow elastic fluids model, Abstract and Applied Analysis, Feb. 2014 view PDF
- Desveaux, V. Zenk, M. Berthon, B. and Klingenberg, C.: 2014: A well-balanced scheme for the Euler equation with a gravitational potential, J. Fuhrmann et al. (eds.), Finite Volumes for Complex Applications VII - Methods and Theoretical Aspects, Springer Proceedings in Mathematics & Statistics 77 view PDF
- Caicedo, J., Klingenberg, C., Lu, Y., Rendon, L.;: 2014: Hyperbolic Approximation on System of Elasticity in Lagrangian Coordinates, Natural Sciences, vol. 6, 6 view PDF
2013:
- Klingenberg, C.: 2013: Grand Challenges in Computational Physics, Frontiers in Computational Physics, vol. 1, view PDF
- Braxmeier-Even, N., Klingenberg, C.: 2013: Continuous sedimentation in clarifier-thickener units: modeling macroscopic conservation laws from microscopic interacting particles, International Journal of Numerical Analysis & Modeling, Series B, Vo. 4, No. 3 view pdf
- Klingenberg, C., Koley, U.: An error estimate for viscous approximate solutions to degenerate anisotropic convection-diffusion equations, AIMS Series on Applied Mathematics
Volume 8, Proceedings of the Fourteenth International Conference on Hyperbolic Problems held in Padova 2012, view PDF
- Hill, A., Joung, M., Mac Low, M., Benjamin, R., Haffner, L., Klingenberg, C., Waagan, K.: 2013, Erratum: Vertical structure of a supernova-driven turbulent, magnetized interstellar medium, to be published in Astrophysics J. view PDF
- Klingenberg, C., Montero, J., Rendón, L.: 2013: Compensated compactness for hyperbolic system of balance laws with three equations, Boletín de Matemáticas, Vol 20, N 1, June 2013. 13-20 view PDF
2012:
- Hill, A., Joung, M., Mac Low, M., Benjamin, R., Haffner, L., Klingenberg, C., Waagan, K.: 2012, Vertical structure of a supernova-driven turbulent, magnetized interstellar medium, Astrophysics J. 750:104 view PDF
- Klingenberg, C, Rendón, L.: 2012: Hölder Estimates of Solutions to a Degenerate Diffusion Equation. preprint
2011:
- Hill, A., Joung, M., Benjamin, R., Haffner, L., Klingenberg, C., Mac Low, M., Waagan,K., Wood. K.: 2011: MHD Simulations of supernovae-driven ISM and Warm ionized medium, Bulletin of the American Astronomical Society, 43 view PDF
- Mac Low, M., Hill, A., Joung, M., Waagan, K., Klingenberg, C., Wood,K., Benjamin, R., Federrath, C., Haffner, L.: 2011, MHD simulations of a supernova-driven ISM and the warm ionized medium using a positivity preserving ideal MHD scheme, Astronomical Society of the Pacific view PDF
- Waagan, K., Federrath, C., Klingenberg, C.: 2011, A robust numerical scheme for highly compressible magnetohydrodynamics: nonlinear stability, implementation and tests, J. Comput. Phys. 230, no. 9 view PDF
2010:
- Pfannes, J., Schmidt, W., Niemeyer, J. Klingenberg, C.: 2010 Thermonuclear explosions of rapidly rotating white dwarfs, Astronomy and Astrophysics 509, A75 view PDF
- Lu, Y., Peng, Y., Klingenberg, C.: 2010, Existence of global solutions to isentropic gas dynamics equations with a source term, Sci. China Math. 53(1): 115–124 view PDF
- Klingenberg, C., Waagan, K.: 2010, Relaxation solvers for ideal MHD equations—a review, Acta Math. Sci. Ser. B Engl. Ed. 30, No. 2 view PDF
- Bouchut, F., Klingenberg, C., Waagan, K.: 2010, A multiwave approximate Riemann solver for ideal MHD based on relaxation II: numerical implementation with 3 and 5 waves. Numer. Math. 115, no. 4 view PDF
2009:
- Lu, Y., Klingenberg, C.: 2009, Singular limits for inhomogeneous equations of elasticity, Acta Math. Sci. Ser. B Engl. Ed. 29, no. 3 view PDF
- Bouchut, F., Klingenberg, C., Waagan, K.: 2009, An approximate Riemann solver for ideal MHD based on relaxation. Hyperbolic problems: theory, numerics and applications, 439–443, Proc. Sympos. Appl. Math., 67, part 2, Amer. Math. Soc., Providence, RI
2008:
- Chen, G.Q., Even, N., Klingenberg, C,: 2008, Hyperbolic conservation laws with discontinuous fluxes and hydrodynamic limit for particle systems, J. Differential Equations 245, no. 11 view PDF
2007:
- Chen, G.Q., Even, N., Klingenberg, C.: 2007, Entropy solutions to conservation laws with discontinuous Fluxes via microscopic interacting particle systems, Stochastic Analysis and Partial Differential Equations, Contemp. Math. Vol. 429, Amer. Math. Soc., RI
- Klingenberg, C, Schmidt, W., Waagan, K.: 2007, Numerical comparison of Riemann solvers for astrophysical hydrodynamics, J. Comput. Phys. 227, No. 1, 12-35 view PDF
- Bouchut, F., Klingenberg, C., Waagan, K.: 2007, A multiwave approximate Riemann solver for ideal MHD based on relaxation. I: Theoretical framework., Numer. Math. 108, No. 1, 7-42 view PDF
- Klingenberg, C.: 2007, Numerical Astrophysics Splinter meeting E, Astronomische Nachrichten Vol. 328, No. 7 view PDF
2005:
Klingenberg, C., Niemeyer, J. C., Schmidt, W., 2005 Modeling Turbulent Deflagrations in Type Ia Supernovae, Nuclear Physics A 758, 431c- 438c view PDF
Klingenberg, C, Schmidt, W., Waagan, K.: 2007, Numerical comparison of Riemann solvers for astrophysical hydrodynamics, J. Comput. Phys. 227, No. 1, 12-35 view PDF
Klingenberg, C., Jabin, P.E.,: 2005, Existence of solutions to an inhomogeneous, kinetic model of droplet coalescence, Nonlinear partial differential equations and related analysis, 181-192, Contemp. Math. Vol. 371, Amer. Math. Soc., RI view PDF
Klingenberg, C., Schütz, G., Tóth, B.: 2005, Mini-workshop: Particle Systems with Several Conservation Laws: Fluctuations and Hydrodynamic Limit, Oberwolfach Reports. Vol. 2, no. 2
Brandenburg, A., Klingenberg, C. Waagan, K.: 2005 The reality of the compound solutions in magnetohydrodynamics, Computational Problems in Physics, Helsinki, ed. Eirola et.al. view PDF
Niemeyer, J., Schmidt, W., Klingenberg, C., Maier, A., Pfannes, J.: 2005, The Birth, Life, and Death of Flames and Detonations in SNe Ia, Bulletin of the American Astronomical Society, Vol. 37
2004:
Grosskinsky, S., Klingenberg, C., Oelschläger: 2004, A rigorous derivation of Smoluchowski’s equation in the moderate limit, Stochastic Analysis and Applications, Vol. 22, No. 1, pp. 113-141 view PDF
Bedjaoui, N., Klingenberg, C., LeFloch, P.: 2004, On the Validity of the Chapman-Enskog Expansion for shock waves with small strength, Portugaliae Mathematica, Vol. 61, No. 4 view PDF
Lu, Y., Klingenberg, C.: 2004 Viscosity and relaxation approximations for a hyperbolic-elliptic mixed type system, Proc. Amer. Math. Soc. 132, no. 5
2003:
Bürger, R., Karlsen, K., Klingenberg, C., Risebro, N.H. : 2003, A front tracking approach to a model of continuous sedimentation in ideal clarifier thickener units, Nonlinear Analysis: Real World Applications, vol 4, pp. 457 - 481 view PDF
Karlsen, K., Klingenberg, C., Risebro, N.H.: 2003, A relaxation scheme for conservation laws with discontinuous coefficients, Math. Comp., Vol 73, No. 247. pp. 1235-1259 view PDF
Klingenberg, C., Lu Y.: 2003 Viscosity and Relaxation Approximations for Hyperbolic-Elliptic Mixed Type System, Proc. AMS, Vol. 132,No. 5 pp. 1305 - 1309 view PDF
Klingenberg, C., Lu, Y.: 2003 A mixed type system of three equations modeling reactive flow Proc. AMS, Vol. 131, No. 11, pp. 3511-3516 view PDF
Karlsen, K., Klingenberg, C., Risebro, N.H. : 2003, Relaxation schemes for conservation laws with discontinuous coefficients, numerical implementation, Hyperbolic problems: Theory, numerics, applications. Proceedings of the ninth international conference on hyperbolic problems, Pasadena, CA, USA, March 25–29, 2002. Berlin: Springer. 611-620
Klingenberg, C., Lu, Y., Zhao H.: 2003 L1 singular limit for relaxation and viscosity approximations of extended traffic flow models, Electronic Journal of Differential Equations, Vol. 2003, No. 23, pp. 1–11 view PDF
Klingenberg, C., Lu, Y., Rendon, L.: 2003 Global Lipshitz-continuous Solutons of Isentropic Gas Dynamics, Applicable Analysis, Vol. 82, No. 1, pp. 35-43 view PDF
2002:
Klingenberg, C. Coquel, F., Pabst, D.: 2002, Solving the Euler equations for high mach number flow, European Series in Applied and Industrial Math. Proc.
Klingenberg, C. : 2002, Computing reactive flow on a coarse grid, Trans. Nanjing Univ. Aeronautics & Astronautics, Vol. 18
Klingenberg, C., Yorke, H. : 2002, Using a Roe solver for simulating astrophysical jets, Proc. of the Phil Roe symposium, in Arcachon, France 1998
2001:
Klingenberg, C., Mitesser, O.: Micro- and macroscopic models of traffic flow. Discrete modeling and discrete algorithms in continuum mechanics (Braunschweig, 2000), 152–156, Logos, Berlin, 2001
Klingenberg, C., Risebro, N. : 2001, Stability of a resonant system of conservation laws modeling polymer flow with gravitation, Journal of Differential Equations, vol. 170, 2, pp. 344-380 view PDF
Klingenberg, C., Lu, Y. : 2001, The relaxation limit for systems of Broadwell type, Differential and Integral Equations, vol. 14, 1 view PDF
D. Serre & J. Shearer, Convergence with physical viscosity for nonlinear elasticity, preprint, never published view PDF
1995 - 2000:
Klingenberg, C., Risebro, N.H. : 1995, Convex conservation laws with discontinuous coefficients, existence, uniqueness, asymptotic behaviour, Comm. P.D.E., vol. 20, no. 11/12 view PDF
Klingenberg, C., Lu, Y. : 1996, Cauchy problem for systems of conservation laws with a relaxation term, Proc. Roy. Soc. Edinb., series A, vol. 126 view PDF
Klingenberg, C., Lu, Y. : 1996, The Cauchy problem for hyperbolic conservation laws with three equations, Journ. Math. Anal. Appl., vol. 202 view PDF
Klingenberg, C., Lu, Y. : 1996, Existence of solutions to resonant systems of conservation laws, Proc. 5th Meet. Hyp. Probl., World Sci. view PDF
Klingenberg, C., Lu, Y.: 1996, The Cauchy problem for conservation laws with relaxation terms, Matematica Contemporanea, vol. 11
Klingenberg, C., Lu, Y. : 1997, Existence to solutions to hyperbolic conservation laws with a source, Comm. Math. Physics, vol. 187, nr. 2 view PDF
Klingenberg, C., Lu, Y. : 1998, The vacuum case in Diperna’s paper, Journ. Math. Anal. Appl., vol. 225, pp. 679-684 view PDF
Klingenberg, C., Lu, Y. : 1999, "The relaxation limit for systems of Broadwell type", in: "Hyperbolic problems: theory, numerics, applications : seventh international conference" in Zürich, February 1998, ed. by Michael Fey; Rolf Jeltsch, Intern. Ser. Num. Math. (Birkh.), vol. 130, pp. 553-557 view PDF
Back, R., Klingenberg, C. : 1999 Numerical methods for multi-fluid Euler equations and its application to an astrophysical jet, Models of Continuum Mechanics in Analysis and Engineering (Shaker)
1990 - 1994:
Klingenberg, C., Plohr, B. : 1991, An introduction to front tracking, IMA Vol. in Math. and Appl., vol. 29, Springer view PDF
Klingenberg, C. : 1991, On shock tracking for hyperbolic conservation laws, Math. & Num. Asp. Wave Prop., SIAM
Klingenberg, C., Zhu, Y.: 1991, On the stability of an initial moving-boundary value problem, Proc. 3rd Meet. Hyp. Probl., Student Litt., Uppsala
Klingenberg, C. : 1991, Front tracking for hyperbolic conservation laws, Usp. Mat. Nauk., vol. 46, no. 6
Klingenberg, C. : 1993, Regularity of scalar Riemann problems in two space dimensions, Notes on Num. Fluid Mech., vol. 43 view PDF
Klingenberg, C., Mao, D.K. : 1994, The total variation decreasing property of conservative front tracking, Math. Comput. Modelling, vol. 20, no. 10/11 view PDF
until 1989:
Klingenberg, C. : 1984, Temporal stability of the Stewartson triple deck, Comm. Amer. Aero. Soc.
Glimm, J., Klingenberg, C. et. al. : 1985, Front tracking, a conference report, Trans. 2nd Army Conf. Appl. Math., SIAM view PDF
Glimm, J., Klingenberg, C. et. al. : 1985, Front tracking and two dimensional Riemann problems, Adv. Appl. Math., vol. 6 view PDF
Klingenberg, C. : 1986, Hyperbolic conservation laws in two space dimensions, Notes on Num. Fluid Mech., Vol. 13
Klingenberg, C. : 1986, Hyperbolic conservation laws: some numerical and theoretical results, Rep. Inst. Mittag-Leffler No. 2
Hsiao, Ling, Klingenberg, C.: 1986, The structure of the solutions for the two dimensional Riemann problem, preprint SFB 123, University of Heidelberg
Klingenberg, C. : 1988, Two dimensional Riemann problems and its applications, Notes on Num. Fluid Mech., Vol. 20
Klingenberg, C., Osher, S. : 1988, Nonconvex scalar conservation laws in one and two space dimensions, Notes on Num. Fluid Mech., Vol. 24 view PDF
Theses:
Klingenberg, C. : 1983, Stability of triple deck flow, PhD thesis, Courant Institute, New York University
Klingenberg, C. : 1992, On the two dimensional Riemann problem for scalar conservation laws, Habilitation, preprint SFB 123, no. 665, University of Heidelberg
submitted:
- Wasilij Barsukow, Janina Kern, Christian Klingenberg, Lisa Lechner: "Analysis of the multi-dimensional semi-discrete Active Flux method using the Fourier transform", submitted (2024) view PDF
- Lena Baumann, Lukas Einkemmer, Christian Klingenberg, Jonas Kusch: "A stable multiplicative dynamical low-rank discretization for the linear Boltzmann-BGK equation", submitted (2024) view PDF
- Kathrin Hellmuth, Christian Klingenberg, Qin Li: "Preserving positivity of Gauss-Newton Hessian through random sampling", submitted (2024) view PDF
- Farah Kanbar, Christian Klingenberg, Min Tang: "Asymptotic and Stationary Preserving Schemes for the Isentropic Euler Equations with Gravitational Source Term", submitted (2024) view PDF
- Yu-Chen Chen, Christian Klingenberg, Rony Touma: “A Well-Balanced Method for an Unstaggered Central Scheme, the two-space Dimensional Case", submitted, (2024) view PDF
- Rony Touma, Elissa Malaeb, Christian Klingenberg: "Unstaggered CWENO with the subtraction method for the shallow water equations", submitted (2024) view PDF
- Yu-Chen Chen, Christian Klingenberg, Rony Touma: “A Well-Balanced Method for an Unstaggered Central Scheme, the one-space Dimensional Case", submitted, (2024) view PDF
2025:
- Junming Duan, Wasilij Barsukow, Christian Klingenberg: “Active flux methods for hyperbolic conservation laws – flux vector splitting and bound-preservation”, SIAM Journal on Scientific Computing (2025) view PDF, supplementary material: view PDF
- Rémi Abgrall, Wasilij Barsukow, Christian Klingenberg: “The Active Flux method for the Euler equations on Cartesian grids", Journal of Scientific Computing, (2025) view PDF view PDF
- Kathrin Hellmuth, Christian Klingenberg, Qin Li, Min Tang: "Reconstructing the kinetic chemotaxis kernel using macroscopic data: well-posedness and ill-posedness", SIAM Journal on Applied Mathematics, (2025) view PDF
- Luis Kaiser, Richard Tsai, Christian Klingenberg: “Efficient Numerical Wave Propagation Enhanced by an End-to-End Deep Learning Model", Proceedings of 'Numerical Mathematics and Advanced Applications (ENUMATH 2023)', Lecture Notes in Computational Science and Engineering, Springer Verlag, (2025) view PDF
2024:
- Yun-guang Lu, Christian Klingenberg, Xiangxing Tao “Global Existence of Entropy Solutions for Euler Equations of Compressible Fluid Flow”, Mathematische Annalen (2024) view PDF
- Rony Touma, Elissa Malaeb, Christian Klingenberg: "Combining a Central Scheme with the Subtraction Method for Shallow Water Equations", International Journal of Computational Methods, Vol. 21, No. 3 (2024) view PDF
- Lena Baumann, Lukas Einkemmer, Christian Klingenberg, Jonas Kusch: "Energy stable and conservative dynamical low-rank approximation for the Su-Olson problem", SIAM Journal on Scientific Computing, vol. 46, no. 2 pp. B137 - B158 (2024) view PDF view PDF
- Claudius Birke, Walter Boscheri, Christian Klingenberg: "A well-balanced semi-implicit IMEX finite volume scheme for ideal Magnetohydrodynamics at all Mach numbers", Journal of Scientific Computing, vol. 98, no. 34, (2024) view PDF
- Kathrin Hellmuth, Christian Klingenberg, Qin Li, Min Tang: "Kinetic chemotaxis tumbling kernel determined from macroscopic quantities", SIAM Journal on Mathematical Analysis, Vol. 56, No. 1, pp. 568-587 (2024) view PDF
- Yun-guang Lu, Jianjun Chen, Weifeng Jiang, Christian Klingenberg, Guoqiao You: “The Global Existence of L∞ Solutions to Isentropic Euler Equations in General Nozzle”, Mathematische Nachrichten, vol. 297, pp. 38–51 (2024) view PDF
- Xianting Wang, Yun-Guang Lu,, Christian Klingenberg: “Viscosity-flux approximation method to inhomogeneous system of isentropic gas dynamics", Journal of Mathematical Analysis and Applications, vol. 531, no. 2 part 2; (2024) view PDF view PDF
- Kathrin Hellmuth, Christian Klingenberg, Qin Li: "Multi-scale PDE inverse problem in bacterial movement", in: Parés, C., Castro, M.J., Morales de Luna, T., Muñoz-Ruiz, M.L. (eds.) Hyperbolic Problems: Theory, Numerics, Applications. Volume II. HYP 2022. SEMA SIMAI Springer Series, vol 35 (2024) view PDF
2023:
- Herzing, T., Klingenberg, C., Pirner, M.: "Hypocoercivity of the linearized BGK-equation with stochastic coefficients", Methods and Applications of Analysis, Vol. 30 No. 3 (2023) view PDF
- Xuanji Jia, Christian Klingenberg, Yun-guang Lu, Qingyou Sun: "Existence of entropy solutions to systems of polytropic gas with a class of unbounded sources", Journal of Nonlinear and Variational Analysis 7, No. 3, pp. 437-448 (2023) view PDF
- Claudius Birke, Christian Klingenberg: "A Low Mach Two-speed Relaxation Scheme for Ideal MHD Equations", Springer Proceedings in Mathematics & Statistics, Finite Volume and Complex Applications X (2023) view PDF
- Claudius Birke, Walter Boscheri, and Christian Klingenberg: "A high order semi-implicit scheme for ideal magnetohydrodynamics", E. Franck et al. (eds.), Finite Volumes for Complex Applications X - Volume 1, Springer Proceedings in Mathematics & Statistics 432 (2023) view PDF
- Yong Chen, Christian Klingenberg, Yun-guang Lu, Xianting Wang, Guoqiao Yo: "Invariant region on a non-isentropic gas dynamics system", Nonlinear Analysis: Real World Applications, Vol. 73 (2023) view PDF
- Claudius Birke and Christian Klingenberg: “Finding an Approximate Riemann Solver via Relaxation: Concept and Advantages", SEMA SIMAI Springer Series: Proceedings of HYP 2022 (2023) view PDF
- Claudius Birke, Christophe Chalons and Christian Klingenberg: “A low Mach two-speed relaxation scheme for the compressible Euler equations with gravity”, Communications in Mathematical Sciences, vol. 21, no. 8, pp. 2213–2246, (2023) view PDF
- Hubert Baty, Florence Drui, Emmanuel Franck, Philippe Helluy, Christian Klingenberg, Lukas Thanhäuser: “A robust and efficient solver based on kinetic schemes for Magnetohydrodynamics (MHD) equations”, Applied Mathematics and Computation, vol. 440 (2023) view PDF view PDF again
- G. Bae, C. Klingenberg, M. Pirner. S. Yun: “BGK model for two-component gases near a global Maxwellian", SIAM Journal on Mathematical Analysis, vol. 55, issue 2 (2023) view PDF view again
- Jeffrey Haack, Cory Hauck, Christian Klingenberg, Marlies Pirner, Sandra Warnecke: "Numerical schemes for a multi-species BGK model with velocity-dependent collision frequency", Journal of Computational Physics, vol. 473 (2023) view PDF
2022:
- Kathrin Hellmuth, Christian Klingenberg, "Route planning for bacteria", 'Snapshots of modern mathematics from Oberwolfach', No. 12 (2022) view PDF
- G. Leidi, C. Birke, R. Andrassy, J. Higl. P. V. F. Edelmann, G. Wiest, C. Klingenberg, F. K. Röpke, "A finite-volume scheme for modelling compressible MHD flows at low Mach numbers in stellar interiors" Astronomy & Astrophysics, vol. 668, no A13 (2022) view PDF
- Farah Kanbar, Christian Klingenberg, Rony Touma: "Well-balanced central scheme for the system of MHD equations with a gravitatonal sorce term", Communications in Computational Physics, vol. 32, no. 3, pp. 878-898 (2022) view PDF
- Manuel Castro, Bruno Després, Michael Dumbser, Christian Klingenberg: "Structure-Preserving Discretizations for Nonlinear Systems of Hyperbolic Equations", Oberwolfach Reports, Vol. 19 (2022) view PDF
- Silu Yin, Xianting Wang, Yun-guang Lu, Christian Klingenberg: "Global solutions of the Cauchy Problem to Euler-Poisson equations of two-carrier types", Applied Mathematics Letters, vol. 132 (2022) view PDF view PDF
- Hahn, B, Kienle-Garrido, Klingenberg, C., Warnecke, S,: “Using the Navier-Cauchy equation for motion estimation in dynamic imaging”, Inverse Probelms and Imaging, vol. 16(5) (2022) view PDF
- E. Feireisl; C. Klingenberg; S. Markfelder, “Euler system with a polytropic equation of state as a vanishing viscosity limit”, Journal of Mathematical Fluid Mechanics, vol. 24, no. 3, paper no. 67 (2022) view PDF
- Hellmuth, K, Klingenberg, C.: “Computing Black Scholes with uncertain volatility - a machine learning approach, Mathematics, vol. 10 (3), 489, special issue "Numerical Analysis with Applications in Machine Learning", ed. P. Tsompanopoulou (2022) view PDF
- Barsukow, W., Klingenberg, C.: “Exact solution and a truly multi-d Godunov scheme for the acoustic equations”, ESAIM: Mathematical Modelling and Numerical Analysis, vol. 56, no. 1, pp. 317 - 347 (2022) view PDF
- Y. Hu, C. Klingenberg; Y. Lu: "Zero relaxation tine limits to a hydrodynamic model of two carrier types for semicinductors": Mathematische Annalen, vol. 383, no. 3-4 (2022) view PDF
2021:
- Kathrin Hellmuth, Christian Klingenberg, Qin Li, Min Tang: "Multiscale convergence of the inverse problem for chemotaxis in the Bayesian setting", Computation, vol. 9, 119, special issue "Inverse Problems with Partial Data”, ed. by Qin Li, Li Wang and Leonardo Andrés Zepeda Núñez (2021) view PDF
- J. Haack, C. Hauck, C. Klingenberg, M. Pirner, S. Warnecke, "A consistent BGK model with velocity-dependent collision frequency for gas mixtures", Journal of Statistical Physics, vol. 84, no. 31 (2021) view PDF
- Barsukow, W. Berberich, J., Klingenberrg, C.: "On the active flux scheme for hyperbolic PDEs with source terms", SIAM Journal on Scientific Computing, vol. 43, no. 6 (2021) view PDE
- Emako, F. Kanbar, C. Klingenberg, M. Tang “A criterion for asymptotic preserving schemes of kinetic equations to be uniformly stationary preserving”, Kinetic and Related models, vol. 14, no. 5 (2021) view PDF
- C. Klingenberg; Y. Lu, C. Xue: "Global entropy solutions for systems modelling polymer flooding in enhanced oil recovery", Applied Mathematics Letters, Vol. 122 (2021) view PDF
- Edelmann, Horst, Berberich, Andrassy, Higl, Leidi, Klingenberg, Röpke: "Well-balanced treatment of gravity in astrophysical fluid dynamics simulations at low Mach numbers", Astronomy & Astrophysics, vol. 652, A53 (2021) view PDF
- Klingenberg, C., Li, Q., Pirner, M.: "Modeling Phenomena from Nature by Hyperbolic Partial Differential Equations", Oberwolfach Reports. vol. 18, no. 2, pp. 1047 - 1085 (2021) view PDF
- Badwaik, J., Klingenberg, C. Risebro, N.H., Ruf, A..: “Multilevel Monte Carlo finite volume methods for random conservation laws with discontinuous flux”, ESAIM: Mathematical Modelling and Numerical Analysis, Vol. 55, No. 3 (2021) view PDF
- Klingenberg, C., Lai, R., Li, Q.: "Reconstruction of the emission coefficient in the nonlinear radiative transfer equation", SIAM Journal on Applied Mathematics, Vol. 81, 1 (2021) view PDE
- Berberich, J., Chandrashekar, P., Klingenberg, C.: “High order well-balanced finite volume methods for multi-dimensional systems of hyperbolic balance laws, Computer and Fluids, Vol. 219 (2021) view PDF
- Berberich, J., Käppeli, R., Chandrashekar, P., Klingenberg, C.: “High order discretely well-balanced methods for arbitrary hydrostatic atmospheres”, Communications in Computational Physics, vol. 30 (2021) view PDF
- G. Bae, C. Klingenberg, M. Pirner. S. Yun: “BGK model of the multi-species Uehling Uhlenbeck equation”, Kinetic and Related Models, Vol. 14, Issue 1 (2021) view PDF
2020:
- J. Berberich, C. Klingenberg: “Entropy Stable Numerical Fluxes for Compressible Euler Equations which are Suitable for All Mach Numbers”, Proceeding of Numhyp 2019, M. L. Muñoz-Ruiz et al. (eds.), Recent Advances in Numerical Methods for Hyperbolic PDE Systems, SEMA SIMAI Springer Series 28 (2020) view PDF
- E. Feireisl; C. Klingenberg; S. Markfelder, “On the density of ‘wild’ initial data for the compressible Euler system”, Calculus of Variations, vol. 59:152 (2020) view PDF
- A. Thomann, G. Puppo, C. Klingenberg, “An all speed second order well-balanced IMEX relaxation scheme for the Euler equations with gravity”, Journal Of Computational Physics, 420 (2020) view PDF view PDF
- C. Klingenberg, O. Kreml, V. Macha and S. Markfelder: “Shocks Make the Riemann Problem for the Full Euler System in Multiple Space Dimensions Ill-posed”, Nonlinearity, Volume 33, Number 12 (2020) view PDF
- Klingenberg, C; Kurganov, A.; Liu, Y.; Zenk, M..: “Moving-Water Equilibria Preserving HLL-Type Schemes for the Shallow Water Equations”, Communications in Mathematical Research, Vol. 36, pp. 247-271 (2020) view PDF
- C. Klingenberg: book review for "Numerical Methods for Conservation Laws: From Analysis to Algorithms" by Jan Hesthaven, SIAM Review (2020) view PDF
- Xue, Klingenberg, Lu, Zhang: “Zero relaxation time limits to isothermal hydrodynamic model for semiconductor”, Applied Mathematics Letters, vol. 109 (2020) view PDF
- Kanbar, Touma, Klingenberg: “Well-balanced Central Schemes for the One and Two-dimensional Euler Systems with Gravity”, Applied Numerical Mathematics, Vol. 156, pp. 608-626, (2020) view PDF view PDF
- A. Thomann, Zenk, M. G. Puppo, C. Klingenberg, “An all speed second order IMEX relaxation scheme for the Euler equations”, Commun. Comp. Phys., Vol. 28, (2020) view PDF
- Q. Sun, Y. Lu, C. Klingenberg: “Global weak solutions for a nonlinear hyperbolic system”, Acta Mathematica Scientia, Ser. B (Engl. Ed.) vol. 40, 5, pp. 1185–1194 (2020) view PDF
- Crestetto, A., Klingenberg, C. Pirner, P.: “Kinetic/Fluid micro-macro numerical scheme for a two component gas mixtures”, SIAM Multiscale Modeling and Simulation, vol. 18 (2) (2020) view PDF
- Volker Springel, Christian Klingenberg, Rüdiger Pakmor, Thomas Guillet, and Praveen Chandrashekar: “Towards exascale simulations of the magnetic universe”, Springer Series Lecture Notes in Computational Science and Engineering "Software for Exa-Scale Computing -- SPPEXA 2016-2019". Springer (2020) view PDF
- C. Klingenberg; S. Markfelder, “Non-uniqueness of entropy-conserving solutions to the ideal compressible MHD equations”, Hyperbolic Problems: Theory, Numerics, Applications, ed. Alberto Bressan, Marta Lewicka, Dehua Wang, Yuxi Zheng, AIMS Series on Applied Mathematics vol. 10 (2020) view PDF
- Baba, Klingenberg, Kreml, Machla, Markfelder: “Non-uniqueness of admissible weak solution to the Riemann problem for the full Euler system in 2D”, SIAM J. Math. Anal., Vol. 52, iss. 2 (2020) view PDF
- Feireisl, E., Klingenberg, C., Kreml, O., Markfelder, S.: “On oscillatory solutions to the complete Euler equations”, Journal of Differential Equations, Vol. 296, issue 2, pp 1521-1543, (2020) view PDF
- Elena Gaburro, Walter Boscheri, Simone Chiocchetti, Christian Klingenberg, Volker Springel, Michael Dumbser: “High order direct Arbitrary-Lagrangian-Eulerian schemes on moving Voronoi meshes with topology changes”, Journal of Computational Physics, Vol. 407 (2020) view PDF
- C. Klingenberg “Relaxation projection solvers - the ultimate approximate Riemann solvers”, in : “Continuum mechanics, applied mathematics and scientific computing: Godunov's legacy - A liber amicorum to Professor Godunov”, ed. Demidenko, Romenski, Toro, Dumbser, Springer Verlag book series: Advanced Structured Materials, (2020) view PDF
- C. Berthon, C. Klingenberg, M. Zenk, “An all Mach number relaxation upwind scheme”, SMAI Journal of Computational Mathematics, Vol. 6 pp. 1 - 31 (2020) view PDF
- Badwaik, J., Chandrashekar, P., Klingenberg, C.: “Single-step Arbitrary Lagrangian-Eulerian discontinuous Galerkin method for 1-D Euler equations”, Communications on Applied Mathematics and Computation vol. 2, pp. 541–579 (2020) view PDF
2019:
- Wasilij Barsukow; Jonathan Hohm; Christian Klingenberg; Philip L Roe, “The active flux scheme on Cartesian grids and its low Mach number limit”, Journal of Scientific Computing. vol. 81, pp. 594–622, (2019) on arXiv , view PDF
- Guermond, J.-L., Klingenberg, C., Popov, B., Tomas, I.: “The Siliciu approximate Riemann solver is not invariant domain preserving”, Journal of Hyperbolic Differential Equations Vol. 16, No. 1 , pp. 1 - 16 (2019) view PDF
- Beyer, T., Moser, E., Heermann, D. W., Klingenberg, C. F., Sauls, J., Valle, J. W. F., de Boer, J., Elizalde, E., Baleanu, D., Hansen, A., Fang, N. X., Pavesi, L., Friedrich, B., Charles, C., Perc, M., Van Der Gucht, J., von Steiger, R., Bogazzi, C., eds.: “Frontiers in Physics - 2017 & 2018, "Editor’s Choice”, Lausanne: Frontiers Media.,(2019) doi: 10.3389/978-2-88945-804-2 (2018) view PDF
- Sun, Lu, Klingenberg,: “Global L^{\infty} Solutions to System of Isentropic Gas Dynamics in a Divergent Nozzle with Friction”, Acta Mathematica Scientia Series B, vol. 39B(5) (2019) view PDF
- Berberich, J., Chandrashekar, P., Klingenberg, C. Röpke, F.: “Second Order Finite Volume Scheme for Euler Equations with Gravity which is Well-Balanced for General Equations of State and Grid Systems”, Communicatons in Compuutational Physics CiCP vol. 26, issue 2, pp. 599-630 (2019) view PDF
- Guillet, Pakmor, Springel, Chandrashekar, Klingenberg, “High-order Magnetohydrodynamics for Astrophysics with an Adaptive Mesh Refinement Discontinuous Galerkin Scheme”, to be published in Monthly Notices of the Royal Astronomical Society, Volume 485, Issue 3, Pages 4209–4246 (2019) view PDF
- Feireisl, E., Klingenberg, Markfelder, S.: “On the low Mach number limit for the compressible Euler system”, SIAM Journal Mathematical Analysis, Vol. 51-2, pp. 1496-1513, (2019) view PDF
- Thomann, A., Zenk, M., Klingenberg, C.,: “A second order well-balanced finite volume scheme for Euler equations with gravity for arbitrary hydrostatic equilibria”, International Journal for Numerical Methods in Fluids, vol. 89, pp. 465–482 (2019) view PDF
- Klingenberg, Pirner, M., Puppo, G. : “A consistent kinetic models for a two-component mixture of polyatomic molecules”, Communication of Mathematical Physics, Vol. 17, No. 1, (2019) view PDF
- C. Klingenberg, G. Puppo, M. Semplice, “Arbitrary order finite volume well-balanced schemes for the Euler equations with gravity”, SIAM J. Scientific Computing,Vol. 41, No. 2, pp. A695-A721 arXiv (2019) view PDF view PDF again