publications (incl. preprints)

submitted:

     - Berberich, J., Käppeli, R., Chandrashekar, P., Klingenberg, C.: “High order discretely well-balanced finite volume methods for Euler equations with gravity - without any a priori information about the hydrostatic solution"”, submitted (2020) view PDF

     - Emako, F. Kanbar, C. Klingenberg, M. Tang  “Asymptotic preserving schemes for kinetic equations that are also stationary preserving”, submitted (2020) 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”, submitted (2020) view PDF

     - J. Berberich, C. Klingenberg: “Entropy Stable Numerical Fluxes for Compressible Euler Equations which are Suitable for All Mach Numbers”, submitted (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”, submitted (2020) view PDF

     - C. Klingenberg; Y. Lu,  Q. Sun: “Viscosity-flux approximation method to inhomogeneous system of isentropic gas dynamics ”, submitted (2020) view PDF

     - C. Klingenberg; Y. Lu,  Q. Sun: “Global L∞ solutions to systems of isentropic gas dynamics with a source term”, submitted (2020) view PDF

     - G. Bae, C. Klingenberg, M. Pirner. S. Yun: “BGK model of the multi-species Uehling Uhlenbeck equation”, submitted (2019) view PDF

     - Berberich, J., Chandrashekar, P., Klingenberg, C.: “High order well-balanced finite volume methods for multi-dimensional systems of hyperbolic balance laws, submitted (2019) view PDF

     - Klingenberg, C; Kurganov, A.; Liu, Y.; Zenk, M..: “Moving-Water Equilibria Preserving HLL-Type Schemes for the Shallow Water Equations ”, submitted (2020)  view PDF

     - E. Feireisl; C. Klingenberg; S. Markfelder, “On the density of ‘wild’ initial data for the compressible Euler system”, submitted (2019)  view PDF

     - Badwaik, J., Klingenberg, C. Risebro, N.H..: “Multilevel Monte Carlo finite volume methods for random conservation laws with discontinuous flux”, submitted (2018) view PDF

     - Barsukow, W., Klingenberg, C.: “Exact solution and a truly multi-d Godunov scheme for the acoustic equations”, preprint (2017) view PDF


2020:

     - Xue, Klingenberg, Lu, Zhang: “Zero relaxation time limits to isothermal hydrodynamic model for semiconductor”, Applied Mathematics Letters (2020) view PDF

     - Kanbar, Touma, Klingenberg: “Well-balanced Central Schemes for the One and Two-dimensional Euler Systems with Gravity”, Applied Numerical Mathematics (2020) 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. (2020) view PDF

     - C. Klingenberg, Y. Lu, Q. Sun: “Global weak solutions for a nonlinear hyperbolic system”, Acta Mathematica Scientia (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, (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. (2020) view PDF

     - Feireisl, E., Klingenberg, C., Kreml, O., Markfelder, S.: “On oscillatory solutions to the complete Euler equations”, Journal of Differential Equations (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 (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”, accepted Communications on Applied Mathematics and Computation (2019)  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 (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.: “Finite volume scheme for Euler equations with gravity which is well-balanced for general equations of state and grid systems”, to appear in Commun. Comput. Phys, (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 (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

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)

view PDF

     - 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

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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