Edit Profile (opens in new tab) Klingenberg, Christian Compute Distance To: Compute Author ID: klingenberg.christian Published as: Klingenberg, Christian; Klingenberg, C. Documents Indexed: 102 Publications since 1985 4 Contributions as Editor Co-Authors: 55 Co-Authors with 63 Joint Publications 1,241 Co-Co-Authors all top 5 Co-Authors 4 single-authored 20 Lu, Yunguang 9 Chandrashekar, Praveen 8 Markfelder, Simon 8 Pirner, Marlies 6 Berberich, Jonas P. 6 Puppo, Gabriella 6 Risebro, Nils Henrik 6 Waagan, Knut 5 Barsukow, Wasilij 5 Zenk, Markus 4 Xia, Yinhua 3 Badwaik, Jayesh 3 Berthon, Christophe 3 Bouchut, François 3 Feireisl, Eduard 3 Karlsen, Kenneth Hvistendahl 3 Kreml, Ondřej 3 Rendón, Leonardo A. 3 Röpke, Friedrich K. 3 Schnücke, Gero 3 Thomann, Andrea 3 Touma, Rony 2 Chen, Gui-Qiang G. 2 Desveaux, Vivien 2 Dumbser, Michael 2 Edelmann, Philipp V. F. 2 Even, Nadine 2 Gallego-Valencia, Juan Pablo 2 Kanbar, Farah 2 Koley, Ujjwal 2 Li, Qin 2 Lu, Xuezhou 2 Mácha, Václav 2 Plohr, Bradley J. 2 Westdickenberg, Michael 2 Xue, Changfeng 1 Al Baba, Hind 1 Annunziato, Mario 1 Bae, Gi-Chan 1 Bedjaoui, Nabil 1 Boileau, Matthieu 1 Borzì, Alfio 1 Boscheri, Walter 1 Bürger, Raimund 1 Castro, Manuel J. 1 Chiocchetti, Simone 1 Colombo, Rinaldo M. 1 Coulette, David 1 Crestetto, Anaïs 1 Després, Bruno 1 Emako, Casimir 1 Federrath, Christoph 1 Franck, Emmanuel 1 Gaburro, Elena 1 Glimm, James G. 1 Großkinsky, Stefan 1 Guermond, Jean-Luc 1 Haack, Jeffrey R. 1 Hauck, Cory D. 1 Helluy, Philippe 1 Hohm, Jonathan 1 Hu, Yanbo 1 Jabin, Pierre-Emmanuel 1 Juajibioy, Juan Carlos 1 Käppeli, Roger 1 Klotzky, Jens 1 Kurganov, Alexander 1 Lai, Ru-Yu 1 LeFloch, Philippe Gerard 1 Liu, Yongle 1 Mao, Dekang 1 McBryan, Oliver A. 1 Meltzer, Marie-Christine 1 Mendoza, Laura S. 1 Miczek, Fabian 1 Mitesser, Oliver 1 Oberlin, Herbert 1 Oelschläger, Karl 1 Osher, Stanley Joel 1 Peng, Yuejun 1 Popov, Boyan 1 Pörner, Frank 1 Roe, Philip L. 1 Roy, Souvik 1 Ruf, Adrian M. 1 Sastoque, Eric Hernandez 1 Schmidt, Wolfram 1 Schütz, Gunter M. 1 Seguin, Nicolas 1 Semplice, Matteo 1 Sharp, David H. 1 Springel, Volker 1 Tomas, Ignacio 1 Tóth, Bálint 1 Warnecke, Sascha 1 Xie, Feng 1 Yaniv, Sara 1 Yun, Seok-Bae 1 Zhang, Jinjun 1 Zhao, Huijiang ...and 1 more Co-Authors all top 5 Serials 4 Journal of Computational Physics 4 Journal of Differential Equations 4 SIAM Journal on Scientific Computing 4 Communications in Computational Physics 3 Mathematics of Computation 3 Journal of Scientific Computing 3 Acta Mathematica Scientia. Series B. (English Edition) 3 Kinetic and Related Models 2 Journal of Mathematical Analysis and Applications 2 Numerische Mathematik 2 Proceedings of the American Mathematical Society 2 Applied Numerical Mathematics 2 Applied Mathematics Letters 2 SIAM Journal on Mathematical Analysis 2 Nonlinear Analysis. Real World Applications 2 Journal of Hyperbolic Differential Equations 2 Oberwolfach Reports 2 European Series in Applied and Industrial Mathematics (ESAIM): Mathematical Modelling and Numerical Analysis 2 Springer Proceedings in Mathematics & Statistics 2 European Series in Applied and Industrial Mathematics (ESAIM): Proceedings and Surveys 1 Applicable Analysis 1 Archive for Rational Mechanics and Analysis 1 Computers and Fluids 1 Communications in Mathematical Physics 1 Journal of Statistical Physics 1 Nonlinearity 1 Mathematische Annalen 1 SIAM Journal on Numerical Analysis 1 Advances in Applied Mathematics 1 Stochastic Analysis and Applications 1 Mathematical and Computer Modelling 1 Differential and Integral Equations 1 Communications in Partial Differential Equations 1 Proceedings of the Royal Society of Edinburgh. Section A. Mathematics 1 SIAM Journal on Applied Mathematics 1 SIAM Review 1 Journal of Partial Differential Equations 1 Computational Optimization and Applications 1 Calculus of Variations and Partial Differential Equations 1 Electronic Journal of Differential Equations (EJDE) 1 Matemática Contemporânea 1 Abstract and Applied Analysis 1 Portugaliae Mathematica. Nova Série 1 Bulletin of the Brazilian Mathematical Society. New Series 1 Multiscale Modeling & Simulation 1 Communications in Mathematical Sciences 1 Analysis and Applications (Singapore) 1 Communications in Mathematical Research 1 Science China. Mathematics 1 SMAI Journal of Computational Mathematics 1 Communications on Applied Mathematics and Computation all top 5 Fields 84 Partial differential equations (35-XX) 57 Fluid mechanics (76-XX) 46 Numerical analysis (65-XX) 15 Statistical mechanics, structure of matter (82-XX) 5 General and overarching topics; collections (00-XX) 4 Probability theory and stochastic processes (60-XX) 3 Classical thermodynamics, heat transfer (80-XX) 3 Astronomy and astrophysics (85-XX) 2 Optics, electromagnetic theory (78-XX) 2 Quantum theory (81-XX) 2 Geophysics (86-XX) 2 Operations research, mathematical programming (90-XX) 1 Calculus of variations and optimal control; optimization (49-XX) 1 Biology and other natural sciences (92-XX) Publications by Year all cited Publications top 5 cited Publications Citations contained in zbMATH Open 63 Publications have been cited 603 times in 279 Documents Cited by ▼ Year ▼ Convex conservation laws with discontinuous coefficients. Existence, uniqueness and asymptotic behavior. Zbl 0836.35090Klingenberg, Christian; Risebro, Nils Henrik 63 1995 A second order well-balanced finite volume scheme for Euler equations with gravity. Zbl 1320.76078Chandrashekar, Praveen; Klingenberg, Christian 34 2015 Stability of a resonant system of conservation laws modeling polymer flow with gravitation. Zbl 0977.35083Klingenberg, Christian; Risebro, Nils Henrik 27 2001 Well-balanced schemes to capture non-explicit steady states: Ripa model. Zbl 1382.65310Desveaux, Vivien; Zenk, Markus; Berthon, Christophe; Klingenberg, Christian 25 2016 A multiwave approximate Riemann solver for ideal MHD based on relaxation. I: Theoretical framework. Zbl 1126.76034Bouchut, François; Klingenberg, Christian; Waagan, Knut 25 2007 A front tracking approach to a model of continuous sedimentation in ideal clarifier-thickener units. Zbl 1013.35052Bürger, R.; Karlsen, K. H.; Klingenberg, C.; Risebro, N. H. 25 2003 A multiwave approximate Riemann solver for ideal MHD based on relaxation. II: Numerical implementation with 3 and 5 waves. Zbl 1426.76338Bouchut, François; Klingenberg, Christian; Waagan, Knut 24 2010 Front tracking and two-dimensional Riemann problems. Zbl 0631.76068Glimm, James; Klingenberg, Christian; McBryan, Oliver; Plohr, Bradley; Sharp, David; Yaniv, Sara 23 1985 Entropy stable finite volume scheme for ideal compressible MHD on 2-D Cartesian meshes. Zbl 1381.76213Chandrashekar, Praveen; Klingenberg, Christian 22 2016 The Riemann problem for the multidimensional isentropic system of gas dynamics is ill-posed if it contains a shock. Zbl 1390.35249Markfelder, Simon; Klingenberg, Christian 22 2018 Well-balanced central finite volume methods for the Ripa system. Zbl 1329.76217Touma, R.; Klingenberg, C. 21 2015 Hyperbolic conservation laws with discontinuous fluxes and hydrodynamic limit for particle systems. Zbl 1195.35211Chen, Gui-Qiang; Even, Nadine; Klingenberg, Christian 18 2008 A numerical scheme for the compressible low-Mach number regime of ideal fluid dynamics. Zbl 1459.65166Barsukow, Wasilij; Edelmann, Philipp V. F.; Klingenberg, Christian; Miczek, Fabian; Röpke, Friedrich K. 17 2017 A well-balanced scheme for the Euler equation with a gravitational potential. Zbl 1304.76027Desveaux, Vivien; Zenk, Markus; Berthon, Christophe; Klingenberg, Christian 16 2014 Arbitrary order finite volume well-balanced schemes for the Euler equations with gravity. Zbl 1412.65125Klingenberg, C.; Puppo, G.; Semplice, M. 16 2019 Existence of solutions to hyperbolic conservation laws with a source. Zbl 0883.35074Klingenberg, Christian; Lu, Yun-guang 15 1997 Arbitrary Lagrangian-Eulerian discontinuous Galerkin method for conservation laws: analysis and application in one dimension. Zbl 1359.65204Klingenberg, Christian; Schnücke, Gero; Xia, Yinhua 15 2017 A robust numerical scheme for highly compressible magnetohydrodynamics: nonlinear stability, implementation and tests. Zbl 1316.76082Waagan, K.; Federrath, C.; Klingenberg, C. 13 2011 A consistent kinetic model for a two-component mixture with an application to plasma. Zbl 1352.82009Klingenberg, Christian; Pirner, Marlies; Puppo, Gabriella 13 2017 On oscillatory solutions to the complete Euler system. Zbl 1437.35557Feireisl, Eduard; Klingenberg, Christian; Kreml, Ondřej; Markfelder, Simon 13 2020 Well-balanced unstaggered central schemes for the Euler equations with gravitation. Zbl 1346.76100Touma, R.; Koley, U.; Klingenberg, C. 11 2016 A relaxation scheme for conservation laws with a discontinuous coefficient. Zbl 1078.65076Karlsen, K. H.; Klingenberg, C.; Risebro, N. H. 10 2004 An arbitrary Lagrangian-Eulerian local discontinuous Galerkin method for Hamilton-Jacobi equations. Zbl 1383.65124Klingenberg, Christian; Schnücke, Gero; Xia, Yinhua 10 2017 A Fokker-Planck approach to control collective motion. Zbl 1390.35362Roy, Souvik; Annunziato, Mario; Borzì, Alfio; Klingenberg, Christian 9 2018 On the low Mach number limit for the compressible Euler system. Zbl 1420.35209Feireisl, Eduard; Klingenberg, Christian; Markfelder, Simon 9 2019 Nonuniqueness of admissible weak solution to the Riemann problem for the full Euler system in two dimensions. Zbl 1437.35474Al Baba, Hind; Klingenberg, Christian; Kreml, Ondřej; Mácha, Václav; Markfelder, Simon 7 2020 A rigorous derivation of Smoluchowski’s equation in the moderate limit. Zbl 1053.60101Großkinsky, S.; Klingenberg, C.; Oelschläger, K. 6 2004 A consistent kinetic model for a two-component mixture of polyatomic molecules. Zbl 1420.35174Klingenberg, Christian; Pirner, Marlies; Puppo, Gabriella 6 2019 Existence, uniqueness and positivity of solutions for BGK models for mixtures. Zbl 1391.35308Klingenberg, C.; Pirner, M. 6 2018 Cauchy problem for hyperbolic conservation laws with a relaxation term. Zbl 0871.35059Klingenberg, Christian; Lu, Yun-guang 5 1996 Numerical comparison of Riemann solvers for astrophysical hydrodynamics. Zbl 1128.85006Klingenberg, Christian; Schmidt, Wolfram; Waagan, Knut 5 2007 The active flux scheme on Cartesian grids and its low Mach number limit. Zbl 1442.65190Barsukow, Wasilij; Hohm, Jonathan; Klingenberg, Christian; Roe, Philip L. 5 2019 A general well-balanced finite volume scheme for Euler equations with gravity. Zbl 1405.76028Berberich, Jonas P.; Chandrashekar, Praveen; Klingenberg, Christian 5 2018 The Cauchy problem for hyperbolic conservation laws with three equations. Zbl 0862.35069Lu, Yunguang; Klingenberg, Christian 4 1996 Relaxation solvers for ideal MHD equations-a review. Zbl 1240.35355Klingenberg, Christian; Waagan, Knut 4 2010 Kinetic ES-BGK models for a multi-component gas mixture. Zbl 1412.65172Klingenberg, Christian; Pirner, Marlies; Puppo, Gabriella 4 2018 A limit problem for three-dimensional ideal compressible radiation magneto-hydrodynamics. Zbl 1386.35361Xie, Feng; Klingenberg, Christian 4 2018 Non-uniqueness of energy-conservative solutions to the isentropic compressible two-dimensional Euler equations. Zbl 1448.76127Klingenberg, Christian; Markfelder, Simon 4 2018 Decay rates for degenerate convection diffusion equations in both one and several space dimensions. Zbl 1340.35140Lu, Yunguang; Klingenberg, Christian; Koley, Ujjwal; Lu, Xuezhou 3 2015 On the density of “wild” initial data for the compressible Euler system. Zbl 1448.76126Feireisl, Eduard; Klingenberg, Christian; Markfelder, Simon 3 2020 Shocks make the Riemann problem for the full Euler system in multiple space dimensions ill-posed. Zbl 1453.35143Klingenberg, Christian; Kreml, Ondřej; Mácha, Václav; Markfelder, Simon 3 2020 A low-Mach Roe-type solver for the Euler equations allowing for gravity source terms. Zbl 1445.35278Barsukow, Wasilij; Edelmann, Philipp V. F.; Klingenberg, Christian; Röpke, Friedrich K. 3 2017 An all speed second order IMEX relaxation scheme for the Euler equations. Zbl 1480.76083Thomann, Andrea; Zenk, Markus; Puppo, Gabriella; Klingenberg, Christian 3 2020 High order well-balanced finite volume methods for multi-dimensional systems of hyperbolic balance laws. Zbl 07426188Berberich, Jonas P.; Chandrashekar, Praveen; Klingenberg, Christian 3 2021 The relaxation limit for systems of Broadwell type. Zbl 1028.35107Lu, Yun-Guang; Klingenberg, Christian 2 2001 A multispecies traffic model based on the Lighthill-Whitham and Richards model. Zbl 1409.35138Colombo, Rinaldo M.; Klingenberg, Christian; Meltzer, Marie-Christine 2 2018 Second order finite volume scheme for Euler equations with gravity which is well-balanced for general equations of state and grid systems. Zbl 07418030Berberich, Jonas P.; Chandrashekar, Praveen; Klingenberg, Christian; Röpke, Friedrich K. 2 2019 An all Mach number relaxation upwind scheme. Zbl 1447.65043Berthon, Christophe; Klingenberg, Christian; Zenk, Markus 2 2020 Reconstruction of the emission coefficient in the nonlinear radiative transfer equation. Zbl 1458.35479Klingenberg, Christian; Lai, Ru-Yu; Li, Qin 2 2021 On limiting for higher order discontinuous Galerkin method for 2D Euler equations. Zbl 1341.35104Gallego-Valencia, Juan Pablo; Klingenberg, Christian; Chandrashekar, Praveen 1 2016 On the validity of Chapman-Enskog expansions for shock waves with small strength. Zbl 1071.35080Bedjaoui, Nabil; Klingenberg, Christian; LeFloch, Philippe G. 1 2004 The vacuum case in DiPerna’s paper. Zbl 0920.76076Klingenberg, Christian; Lu, Yun-Guang 1 1998 The relaxation limit for systems of broadwell type. Zbl 0926.35079Klingenberg, Christian; Lu, Yun-Guang 1 1999 Existence to solutions of a kinetic aerosol model. Zbl 1083.35057Jabin, Pierre-Emmanuel; Klingenberg, Christian 1 2005 Viscosity and relaxation approximations for a hyperbolic-elliptic mixed type system. Zbl 1037.35045Lu, Yunguang; Klingenberg, Christian 1 2004 On well-posedness for a multi-particle fluid model. Zbl 1410.35126Klingenberg, Christian; Klotzky, Jens; Seguin, Nicolas 1 2018 Kinetic/fluid micro-macro numerical scheme for a two component gas mixture. Zbl 1446.65137Crestetto, Anaïs; Klingenberg, Christian; Pirner, Marlies 1 2020 Task-based parallelization of an implicit kinetic scheme. Zbl 1408.35143Badwaik, Jayesh; Boileau, Matthieu; Coulette, David; Franck, Emmanuel; Helluy, Philippe; Klingenberg, Christian; Mendoza, Laura; Oberlin, Herbert 1 2018 Well-balanced central schemes for the one and two-dimensional Euler systems with gravity. Zbl 1442.65199Kanbar, F.; Touma, R.; Klingenberg, C. 1 2020 Moving-water equilibria preserving HLL-type schemes for the shallow water equations. Zbl 1463.76035Klingenberg, Christian; Kurganov, Alexander; Liu, Yongle; Zenk, Markus 1 2020 An efficient implementation of the divergence free constraint in a discontinuous Galerkin method for magnetohydrodynamics on unstructured meshes. Zbl 07413979Klingenberg, Christian; Pörner, Frank; Xia, Yinhua 1 2017 A criterion for asymptotic preserving schemes of kinetic equations to be uniformly stationary preserving. Zbl 1476.65205Emako, Casimir; Kanbar, Farah; Klingenberg, Christian; Tang, Min 1 2021 Exact solution and the multidimensional Godunov scheme for the acoustic equations. Zbl 07488296Barsukow, Wasilij; Klingenberg, Christian 1 2022 Exact solution and the multidimensional Godunov scheme for the acoustic equations. Zbl 07488296Barsukow, Wasilij; Klingenberg, Christian 1 2022 High order well-balanced finite volume methods for multi-dimensional systems of hyperbolic balance laws. Zbl 07426188Berberich, Jonas P.; Chandrashekar, Praveen; Klingenberg, Christian 3 2021 Reconstruction of the emission coefficient in the nonlinear radiative transfer equation. Zbl 1458.35479Klingenberg, Christian; Lai, Ru-Yu; Li, Qin 2 2021 A criterion for asymptotic preserving schemes of kinetic equations to be uniformly stationary preserving. Zbl 1476.65205Emako, Casimir; Kanbar, Farah; Klingenberg, Christian; Tang, Min 1 2021 On oscillatory solutions to the complete Euler system. Zbl 1437.35557Feireisl, Eduard; Klingenberg, Christian; Kreml, Ondřej; Markfelder, Simon 13 2020 Nonuniqueness of admissible weak solution to the Riemann problem for the full Euler system in two dimensions. Zbl 1437.35474Al Baba, Hind; Klingenberg, Christian; Kreml, Ondřej; Mácha, Václav; Markfelder, Simon 7 2020 On the density of “wild” initial data for the compressible Euler system. Zbl 1448.76126Feireisl, Eduard; Klingenberg, Christian; Markfelder, Simon 3 2020 Shocks make the Riemann problem for the full Euler system in multiple space dimensions ill-posed. Zbl 1453.35143Klingenberg, Christian; Kreml, Ondřej; Mácha, Václav; Markfelder, Simon 3 2020 An all speed second order IMEX relaxation scheme for the Euler equations. Zbl 1480.76083Thomann, Andrea; Zenk, Markus; Puppo, Gabriella; Klingenberg, Christian 3 2020 An all Mach number relaxation upwind scheme. Zbl 1447.65043Berthon, Christophe; Klingenberg, Christian; Zenk, Markus 2 2020 Kinetic/fluid micro-macro numerical scheme for a two component gas mixture. Zbl 1446.65137Crestetto, Anaïs; Klingenberg, Christian; Pirner, Marlies 1 2020 Well-balanced central schemes for the one and two-dimensional Euler systems with gravity. Zbl 1442.65199Kanbar, F.; Touma, R.; Klingenberg, C. 1 2020 Moving-water equilibria preserving HLL-type schemes for the shallow water equations. Zbl 1463.76035Klingenberg, Christian; Kurganov, Alexander; Liu, Yongle; Zenk, Markus 1 2020 Arbitrary order finite volume well-balanced schemes for the Euler equations with gravity. Zbl 1412.65125Klingenberg, C.; Puppo, G.; Semplice, M. 16 2019 On the low Mach number limit for the compressible Euler system. Zbl 1420.35209Feireisl, Eduard; Klingenberg, Christian; Markfelder, Simon 9 2019 A consistent kinetic model for a two-component mixture of polyatomic molecules. Zbl 1420.35174Klingenberg, Christian; Pirner, Marlies; Puppo, Gabriella 6 2019 The active flux scheme on Cartesian grids and its low Mach number limit. Zbl 1442.65190Barsukow, Wasilij; Hohm, Jonathan; Klingenberg, Christian; Roe, Philip L. 5 2019 Second order finite volume scheme for Euler equations with gravity which is well-balanced for general equations of state and grid systems. Zbl 07418030Berberich, Jonas P.; Chandrashekar, Praveen; Klingenberg, Christian; Röpke, Friedrich K. 2 2019 The Riemann problem for the multidimensional isentropic system of gas dynamics is ill-posed if it contains a shock. Zbl 1390.35249Markfelder, Simon; Klingenberg, Christian 22 2018 A Fokker-Planck approach to control collective motion. Zbl 1390.35362Roy, Souvik; Annunziato, Mario; Borzì, Alfio; Klingenberg, Christian 9 2018 Existence, uniqueness and positivity of solutions for BGK models for mixtures. Zbl 1391.35308Klingenberg, C.; Pirner, M. 6 2018 A general well-balanced finite volume scheme for Euler equations with gravity. Zbl 1405.76028Berberich, Jonas P.; Chandrashekar, Praveen; Klingenberg, Christian 5 2018 Kinetic ES-BGK models for a multi-component gas mixture. Zbl 1412.65172Klingenberg, Christian; Pirner, Marlies; Puppo, Gabriella 4 2018 A limit problem for three-dimensional ideal compressible radiation magneto-hydrodynamics. Zbl 1386.35361Xie, Feng; Klingenberg, Christian 4 2018 Non-uniqueness of energy-conservative solutions to the isentropic compressible two-dimensional Euler equations. Zbl 1448.76127Klingenberg, Christian; Markfelder, Simon 4 2018 A multispecies traffic model based on the Lighthill-Whitham and Richards model. Zbl 1409.35138Colombo, Rinaldo M.; Klingenberg, Christian; Meltzer, Marie-Christine 2 2018 On well-posedness for a multi-particle fluid model. Zbl 1410.35126Klingenberg, Christian; Klotzky, Jens; Seguin, Nicolas 1 2018 Task-based parallelization of an implicit kinetic scheme. Zbl 1408.35143Badwaik, Jayesh; Boileau, Matthieu; Coulette, David; Franck, Emmanuel; Helluy, Philippe; Klingenberg, Christian; Mendoza, Laura; Oberlin, Herbert 1 2018 A numerical scheme for the compressible low-Mach number regime of ideal fluid dynamics. Zbl 1459.65166Barsukow, Wasilij; Edelmann, Philipp V. F.; Klingenberg, Christian; Miczek, Fabian; Röpke, Friedrich K. 17 2017 Arbitrary Lagrangian-Eulerian discontinuous Galerkin method for conservation laws: analysis and application in one dimension. Zbl 1359.65204Klingenberg, Christian; Schnücke, Gero; Xia, Yinhua 15 2017 A consistent kinetic model for a two-component mixture with an application to plasma. Zbl 1352.82009Klingenberg, Christian; Pirner, Marlies; Puppo, Gabriella 13 2017 An arbitrary Lagrangian-Eulerian local discontinuous Galerkin method for Hamilton-Jacobi equations. Zbl 1383.65124Klingenberg, Christian; Schnücke, Gero; Xia, Yinhua 10 2017 A low-Mach Roe-type solver for the Euler equations allowing for gravity source terms. Zbl 1445.35278Barsukow, Wasilij; Edelmann, Philipp V. F.; Klingenberg, Christian; Röpke, Friedrich K. 3 2017 An efficient implementation of the divergence free constraint in a discontinuous Galerkin method for magnetohydrodynamics on unstructured meshes. Zbl 07413979Klingenberg, Christian; Pörner, Frank; Xia, Yinhua 1 2017 Well-balanced schemes to capture non-explicit steady states: Ripa model. Zbl 1382.65310Desveaux, Vivien; Zenk, Markus; Berthon, Christophe; Klingenberg, Christian 25 2016 Entropy stable finite volume scheme for ideal compressible MHD on 2-D Cartesian meshes. Zbl 1381.76213Chandrashekar, Praveen; Klingenberg, Christian 22 2016 Well-balanced unstaggered central schemes for the Euler equations with gravitation. Zbl 1346.76100Touma, R.; Koley, U.; Klingenberg, C. 11 2016 On limiting for higher order discontinuous Galerkin method for 2D Euler equations. Zbl 1341.35104Gallego-Valencia, Juan Pablo; Klingenberg, Christian; Chandrashekar, Praveen 1 2016 A second order well-balanced finite volume scheme for Euler equations with gravity. Zbl 1320.76078Chandrashekar, Praveen; Klingenberg, Christian 34 2015 Well-balanced central finite volume methods for the Ripa system. Zbl 1329.76217Touma, R.; Klingenberg, C. 21 2015 Decay rates for degenerate convection diffusion equations in both one and several space dimensions. Zbl 1340.35140Lu, Yunguang; Klingenberg, Christian; Koley, Ujjwal; Lu, Xuezhou 3 2015 A well-balanced scheme for the Euler equation with a gravitational potential. Zbl 1304.76027Desveaux, Vivien; Zenk, Markus; Berthon, Christophe; Klingenberg, Christian 16 2014 A robust numerical scheme for highly compressible magnetohydrodynamics: nonlinear stability, implementation and tests. Zbl 1316.76082Waagan, K.; Federrath, C.; Klingenberg, C. 13 2011 A multiwave approximate Riemann solver for ideal MHD based on relaxation. II: Numerical implementation with 3 and 5 waves. Zbl 1426.76338Bouchut, François; Klingenberg, Christian; Waagan, Knut 24 2010 Relaxation solvers for ideal MHD equations-a review. Zbl 1240.35355Klingenberg, Christian; Waagan, Knut 4 2010 Hyperbolic conservation laws with discontinuous fluxes and hydrodynamic limit for particle systems. Zbl 1195.35211Chen, Gui-Qiang; Even, Nadine; Klingenberg, Christian 18 2008 A multiwave approximate Riemann solver for ideal MHD based on relaxation. I: Theoretical framework. Zbl 1126.76034Bouchut, François; Klingenberg, Christian; Waagan, Knut 25 2007 Numerical comparison of Riemann solvers for astrophysical hydrodynamics. Zbl 1128.85006Klingenberg, Christian; Schmidt, Wolfram; Waagan, Knut 5 2007 Existence to solutions of a kinetic aerosol model. Zbl 1083.35057Jabin, Pierre-Emmanuel; Klingenberg, Christian 1 2005 A relaxation scheme for conservation laws with a discontinuous coefficient. Zbl 1078.65076Karlsen, K. H.; Klingenberg, C.; Risebro, N. H. 10 2004 A rigorous derivation of Smoluchowski’s equation in the moderate limit. Zbl 1053.60101Großkinsky, S.; Klingenberg, C.; Oelschläger, K. 6 2004 On the validity of Chapman-Enskog expansions for shock waves with small strength. Zbl 1071.35080Bedjaoui, Nabil; Klingenberg, Christian; LeFloch, Philippe G. 1 2004 Viscosity and relaxation approximations for a hyperbolic-elliptic mixed type system. Zbl 1037.35045Lu, Yunguang; Klingenberg, Christian 1 2004 A front tracking approach to a model of continuous sedimentation in ideal clarifier-thickener units. Zbl 1013.35052Bürger, R.; Karlsen, K. H.; Klingenberg, C.; Risebro, N. H. 25 2003 Stability of a resonant system of conservation laws modeling polymer flow with gravitation. Zbl 0977.35083Klingenberg, Christian; Risebro, Nils Henrik 27 2001 The relaxation limit for systems of Broadwell type. Zbl 1028.35107Lu, Yun-Guang; Klingenberg, Christian 2 2001 The relaxation limit for systems of broadwell type. Zbl 0926.35079Klingenberg, Christian; Lu, Yun-Guang 1 1999 The vacuum case in DiPerna’s paper. Zbl 0920.76076Klingenberg, Christian; Lu, Yun-Guang 1 1998 Existence of solutions to hyperbolic conservation laws with a source. Zbl 0883.35074Klingenberg, Christian; Lu, Yun-guang 15 1997 Cauchy problem for hyperbolic conservation laws with a relaxation term. Zbl 0871.35059Klingenberg, Christian; Lu, Yun-guang 5 1996 The Cauchy problem for hyperbolic conservation laws with three equations. Zbl 0862.35069Lu, Yunguang; Klingenberg, Christian 4 1996 Convex conservation laws with discontinuous coefficients. Existence, uniqueness and asymptotic behavior. Zbl 0836.35090Klingenberg, Christian; Risebro, Nils Henrik 63 1995 Front tracking and two-dimensional Riemann problems. Zbl 0631.76068Glimm, James; Klingenberg, Christian; McBryan, Oliver; Plohr, Bradley; Sharp, David; Yaniv, Sara 23 1985 all cited Publications top 5 cited Publications all top 5 Cited by 379 Authors 23 Klingenberg, Christian 18 Karlsen, Kenneth Hvistendahl 17 Risebro, Nils Henrik 12 Bürger, Raimund 12 Lu, Yunguang 11 Chandrashekar, Praveen 10 Mishra, Siddhartha 8 Towers, John D. 7 Adimurthi, A. 7 Barsukow, Wasilij 7 Bouchut, François 7 Gowda, G. D. Veerappa 6 Diehl, Stefan 6 Gassner, Gregor J. 6 Winters, Andrew R. 5 Berberich, Jonas P. 5 Bermúdez, Alfredo 5 Berthon, Christophe 5 Castro, Manuel J. 5 Chalons, Christophe 5 Chen, Gui-Qiang G. 5 Dumbser, Michael 5 Mai Duc Thanh 5 Wang, Guodong 5 Wu, Kailiang 4 Capdeville, Guy 4 Derigs, Dominik 4 Feldman, Mikhail 4 Lhébrard, Xavier 4 Li, Gang 4 López, Xián 4 Puppo, Gabriella 4 Seguin, Nicolas 4 Shen, Wen 4 Shu, Chi-Wang 4 Vázquez-Cendón, María Elena 4 Waagan, Knut 4 Walch, Stefanie 3 Amadori, Debora 3 Gaburro, Elena 3 Ghoshal, Shyam Sundar 3 Gosse, Laurent 3 Guerra, Graziano 3 Gwiazda, Piotr 3 Käppeli, Roger 3 Kurganov, Alexander 3 LeFloch, Philippe Gerard 3 Menikoff, Ralph 3 Noelle, Sebastian 3 Parés Madroñal, Carlos 3 Plohr, Bradley J. 3 Qian, Shouguo 3 Raviart, Pierre-Arnaud 3 Shen, Chun 3 Sjogreen, Bjorn 3 Sun, Meina 3 Świerczewska-Gwiazda, Agnieszka 3 Thanh, Nguyen Xuan 3 Touma, Rony 3 Xing, Yulong 3 Yee, Helen C. 3 Zenk, Markus 2 Abbate, Emanuela 2 Badwaik, Jayesh 2 Boutin, Benjamin 2 Boyaval, Sébastien 2 Brull, Stephane 2 Bukiet, Bruce G. 2 Busto, Saray 2 Chertock, Alina E. 2 Coclite, Giuseppe Maria 2 Coquel, Frédéric 2 Cui, Shumo 2 Cuong, Dao Huy 2 Feireisl, Eduard 2 Foucher, Françoise 2 Franck, Emmanuel 2 Fuchs, Franz Georg 2 Goatin, Paola 2 Godlewski, Edwige 2 Grove, John W. 2 Hammond, Alan 2 Helzel, Christiane 2 Hu, Yanbo 2 Iollo, Angelo 2 Jin, Shi 2 Jung, Jonathan 2 Kanbar, Farah 2 Kerkmann, David 2 Kumar Kenettinkara, Sudarshan 2 Kumar, Rakesh 2 Li, Jiaojiao 2 Lu, Xuezhou 2 Lukáčová-Medvid’ová, Mária 2 Markfelder, Simon 2 Meena, Asha Kumari 2 Michel-Dansac, Victor 2 Rezakhanlou, Fraydoun 2 Roe, Philip L. 2 Röpke, Friedrich K. ...and 279 more Authors all top 5 Cited in 83 Serials 36 Journal of Computational Physics 19 Journal of Scientific Computing 16 Computers and Fluids 16 Journal of Differential Equations 11 SIAM Journal on Scientific Computing 9 Applied Mathematics and Computation 9 M\(^3\)AS. Mathematical Models & Methods in Applied Sciences 8 Mathematics of Computation 8 Numerische Mathematik 8 Journal of Hyperbolic Differential Equations 7 Journal of Engineering Mathematics 7 Communications in Computational Physics 6 Applied Numerical Mathematics 5 Computers & Mathematics with Applications 5 Applied Mathematics Letters 5 SIAM Journal on Mathematical Analysis 5 European Series in Applied and Industrial Mathematics (ESAIM): Mathematical Modelling and Numerical Analysis 4 Journal of Computational and Applied Mathematics 4 Nonlinear Analysis. Real World Applications 3 Archive for Rational Mechanics and Analysis 3 Journal of Mathematical Analysis and Applications 3 ZAMP. Zeitschrift für angewandte Mathematik und Physik 3 SIAM Journal on Numerical Analysis 3 Networks and Heterogeneous Media 3 SMAI Journal of Computational Mathematics 2 Proceedings of the American Mathematical Society 2 Advances in Applied Mathematics 2 Stochastic Processes and their Applications 2 Advances in Computational Mathematics 2 International Journal of Nonlinear Sciences and Numerical Simulation 2 Bulletin of the Malaysian Mathematical Sciences Society. Second Series 2 Science China. Mathematics 2 European Series in Applied and Industrial Mathematics (ESAIM): Proceedings and Surveys 1 Computer Methods in Applied Mechanics and Engineering 1 Communications on Pure and Applied Mathematics 1 International Journal of Engineering Science 1 Jahresbericht der Deutschen Mathematiker-Vereinigung (DMV) 1 Journal of Fluid Mechanics 1 Nonlinearity 1 Reviews of Modern Physics 1 Physics of Fluids, A 1 The Annals of Probability 1 International Journal for Numerical Methods in Engineering 1 Inventiones Mathematicae 1 Journal of Functional Analysis 1 Meccanica 1 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods 1 Quarterly of Applied Mathematics 1 Acta Applicandae Mathematicae 1 Annales de l’Institut Henri Poincaré. Analyse Non Linéaire 1 Acta Mathematicae Applicatae Sinica. English Series 1 Mathematical and Computer Modelling 1 Science in China. Series A 1 The Annals of Applied Probability 1 Applied Mathematical Modelling 1 Communications in Partial Differential Equations 1 Journal of Elasticity 1 Proceedings of the National Academy of Sciences of the United States of America 1 SIAM Journal on Applied Mathematics 1 Annales de l’Institut Henri Poincaré. Probabilités et Statistiques 1 Journal of Nonlinear Science 1 Computational Optimization and Applications 1 Topological Methods in Nonlinear Analysis 1 Computational and Applied Mathematics 1 Monte Carlo Methods and Applications 1 Computing and Visualization in Science 1 International Journal of Computational Fluid Dynamics 1 European Series in Applied and Industrial Mathematics (ESAIM): Proceedings 1 Abstract and Applied Analysis 1 Taiwanese Journal of Mathematics 1 Journal of Applied Mechanics and Technical Physics 1 Journal of Shanghai University 1 Annals of Mathematics. Second Series 1 M2AN. Mathematical Modelling and Numerical Analysis. ESAIM, European Series in Applied and Industrial Mathematics 1 Acta Mathematica Scientia. Series B. (English Edition) 1 Bulletin of the Brazilian Mathematical Society. New Series 1 Analysis and Applications (Singapore) 1 Acta Numerica 1 Confluentes Mathematici 1 Advances in Applied Mathematics and Mechanics 1 Bulletin of Mathematical Sciences 1 SIAM/ASA Journal on Uncertainty Quantification 1 Iranian Journal of Numerical Analysis and Optimization all top 5 Cited in 21 Fields 187 Partial differential equations (35-XX) 176 Fluid mechanics (76-XX) 141 Numerical analysis (65-XX) 10 Probability theory and stochastic processes (60-XX) 10 Mechanics of deformable solids (74-XX) 8 Statistical mechanics, structure of matter (82-XX) 8 Geophysics (86-XX) 6 Operations research, mathematical programming (90-XX) 5 Astronomy and astrophysics (85-XX) 4 Biology and other natural sciences (92-XX) 3 Calculus of variations and optimal control; optimization (49-XX) 3 Classical thermodynamics, heat transfer (80-XX) 2 Dynamical systems and ergodic theory (37-XX) 2 Operator theory (47-XX) 2 Mechanics of particles and systems (70-XX) 2 Optics, electromagnetic theory (78-XX) 1 Real functions (26-XX) 1 Difference and functional equations (39-XX) 1 Harmonic analysis on Euclidean spaces (42-XX) 1 Functional analysis (46-XX) 1 Relativity and gravitational theory (83-XX) Citations by Year