Publications

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, 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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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)

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

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

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