Articles in Preparation
| 5. | A.M. Rueda-Ramírez, F.J. Hindenlang, J. Chan, and G.J. Gassner. Entropy-Stable Gauss Collocation Methods for Ideal Magneto-Hydrodynamics, submitted to Journal of Computational Physics. |
| 4. | D.A. Kopriva, G.J. Gassner, and J. Nordström. On the Theoretical Foundation of Overset Grid Methods for Hyperbolic Problems II: Entropy Bounded Formulations for Nonlinear Conservation Laws, submitted to Journal of Computational Physics. |
| 3. | L.M. Versbach, P. Birken, V. Linders, G.J. Gassner. Local Fourier Analysis of a Space-Time Multigrid Method for DG-SEM for the Linear Advection Equation, submitted to Electronic Transactions on Numerical Analysis. |
| 2. | A.M. Rueda-Ramirez, W. Pazner, and G.J. Gassner. Subcell Limiting Strategies for Discontinuous Galerkin Spectral Element Methods, submitted to Computers and Fluids. |
| 1. | H. Ranocha, M. Schlottke-Lakemper, J. Chan, A.M. Rueda-Ramirez, A. R. Winters, F. Hindenlang, G.J. Gassner. Efficient implementation of modern entropy stable and kinetic energy preserving discontinuous Galerkin methods for conservation laws, submitted to ACM Transactions on Mathematical Software. |
Accepted and Published Articles (Peer-Review)
| 71. | J. Chan, H. Ranocha, A. Rueda-Ramirez, G.J. Gassner, and T. Warburton. On the entropy projection and the robustness of high order entropy stable discontinuous Galerkin schemes for under-resolved flows. Accepted in Frontier in Physics 2022. |
| 70. | J. Markert, S. Walch, and G.J. Gassner. A Discontinuous Galerkin Solver in the FLASH Multi-Physics Framework. Accepted in Monthly Notices of the Royal Astronomical Society Main Journal 2022. |
| 69. | H. Ranocha, M. Schlottke-Lakemper, A.R. Winters, E. Faulhaber, J. Chan, and G.J. Gassner. Adaptive numerical simulations with Trixi.jl: A case study of Julia for scientific computing. JuliaCon Proceedings, 1(1), 77, 2022. |
| 68. | D.A. Kopriva, J. Nordström, and G.J. Gassner. On the Theoretical Foundation of Overset Grid Methods for Hyperbolic Problems: Well-Posedness and Conservation. Journal of Computational Physics, Volume 448, 2022. |
| 67. | G.J. Gassner, M. Svärd, and F.J. Hindenlang. Stability issues of entropy-stable and/or split-form high-order schemes. Journal of Scientific Computing, Volume 90(3), 2022. |
| 66. | D.A. Kopriva and G.J. Gassner. A Split-Form, Stable CG/DG-SEM for Wave Propagation Modeled by Linear Hyperbolic Systems. Journal of Scientific Computing, Volume 89, 2021. |
| 65. | A.M. Rueda-Ramirez, S. Heinemann, F.J. Hindenlang, A.R. Winters, G.J. Gassner. An Entropy Stable Nodal Discontinuous Galerkin Method for the resistive MHD Equations. Part II: Subcell Finite Volume Shock Capturing. Journal of Computational Physics, Volume 444, 2021. |
| 64. | D. Kopriva, G.J. Gassner, and J. Nordström. Stability of Discontinuous Galerkin Spectral Element Schemes for Wave Propagation when the Coefficient Matrices have Jumps. Journal of Scientific Computing, Volume 88, 2021. |
| 63. | H. Ranocha and G.J. Gassner. Perventing pressure oscillations does not fix local linear stability issues of entropy-based split-form hight-order schemes. Communications in Applied Mathematics and Computation, doi.org/10.1007/s42967-021-00148-z, 2021. |
| 62. | J. Markert, G. Gassner, and S. Walch. A Sub-element Adaptive Shock capturing Approach for Discontinuous Galerkin Methods. Communications in Applied Mathematics, doi.org/10.1000/s42967-021-00120-x, 2021. |
| 61. | M. Schlottke-Lakemper, A.R. Winters, H. Ranocha, and G.J. Gassner. A purely hyperbolic discontinuous Galerkin approach for self-gravitating gas dynamics. Journal of Computational Physics, Vol. 442, 2021. |
| 60. | S. Hennemann and G.J. Gassner. A provably entropy stable subcell shock capturing approach for high order split form DG. Journal of Computational Physics, Vol. 426, 2021. |
| 59. | G.J. Gassner and A.R. Winters. A Novel Robust Strategy for Discontinuous Galerkin Methods in Computational Physics: Why? When? What? Where? Frontiers in Physics - Rising Stars, 2021. |
| 58. | N. Krais, A. Beck, T. Bolemann, H. Frank, D. Flad, G.J. Gassner, F. Hindenlang, M. Hoffmann, T. Kuhn, M. Sonntag, C.-D. Munz. FLEXI: A high order discontinuous Galerkin framework for hyperbolic-parabolic conservation laws. Computers & Mathematics with Applications, Vol. 81: 186-219, 2021. |
| 57. | D. Del Rey Fernández, M.H. Carpenter, L. Friedrich, L. Dalcin, A.R. Winters, G.J. Gassner and M. Parsani. Entropy Stable Non-conforming Discretization with the Summation-by-Parts Property for the Compressible Navier-Stokes equations. Computers & Fluids, Vol. 210, 2020. |
| 56. | N. Krais, G. Schnuecke, T. Bolemann and G.J. Gassner. Split form ALE discontinuous Galerkin methods with applications to under-resolved turbulent low-Mach number flows. Journal of Computational Physics, Vol. 421, 2020. |
| 55. | A.R. Winters, C. Czernik, M. Schily and G.J. Gassner. Entropy stable numerical approximations for the isothermal and polytropic Euler equations. BIT Numerical Mathematics, Vol. 60: 791-824, 2020. |
| 54. | G. Schnuecke, N. Krais, T. Bolemann and G.J. Gassner. Entropy Stable Discontinuous Galerkin Schemes on Moving Meshes with Summation-by-Parts Property for Hyperbolic Conservation Laws. Journal of Scientific Computing, Vol. 82, Article number: 69, 2020. |
| 53. | M. Bohm, A.R. Winters, G.J. Gassner, D. Derigs, F. Hindenlang, J.Saur. An entropy stable nodal discontinuous Galerkin method for the resistive MHD equations. Part I: Theory and Numerical Verification. Journal of Computational Physics, Vol. 422, 2020. |
| 52. | A.R. Winters, M. Bohm, S. Schermeng, G.J. Gassner and G.B. Jacobs. Multi-element SIAC filter for shock capturing applied to high-order discontinuous Galerkin spectral element methods. Journal of Scientific Computing, Vol. 81: 820-844, 2019. |
| 51. | L. Friedrich, G. Schnuecke, A.R. Winters, D.C. Del Rey Fernández, G.J. Gassner, M.H. Carpenter. Entropy Stable Space-Time Discontinuous Galerkin Schemes with Summation-by-Parts Property for Hyperbolic Conservation Laws. Journal of Scientific Computing, Vol. 80: 175-222, 2019. |
| 50. | P. Birken, L.M. Versbach and G.J. Gassner. Subcell Finite Volume Multigrid Preconditioning for High Order Discontinuous Galerkin Methods. International Journal of Computational Fluid Dynamics, Vol. 33: 353-361, 2019. |
| 49. | D. Kopriva, F. Hindenlang, T. Boleman and G.J. Gassner. Free-Stream Preservation for Curved Geometrically Non-Conforming Discontinuous Galerkin Spectral Elements. Journal of Scientific Computing, Vol. 79: 1389-1408, 2019. |
| 48. | L.M. Versbach, P. Birken and G.J. Gassner. Finite volume based multigrid preconditioners for discontinuous Galerkin methods. PAMM, Vol. 18, 2018. |
| 47. | N. Wintermeyer, A R. Winters, G.J. Gassner, and T. Warburton. An Entropy Stable Discontinuous Galerkin Method for the Shallow Water Equations on Curvilinear Meshes with Wet/Dry Fronts Accelerated by GPUs. Journal of Computational Physics, Vol. 375: 447-480, 2018. |
| 46. | A.R. Winters, R.C. Moura, G. Mengaldo, G.J. Gassner, S. Walch, J. Peiro, S.J. Sherwin. A comparative study on polynomial dealiasing and split form discontinuous Galerkin schemes for under-resolved turbulence computations. Journal of Computational Physics, Vol. 372: 1-21, 2018. |
| 45. | G.J. Gassner, A R. Winters, F. Hindenlang, D.A. Kopriva. The BR1 Scheme is Stable for the Compressible Navier-Stokes Equations. Journal of Scientific Computing, Vol. 77: 154-200, 2018. |
| 44. | D. Derigs, G.J. Gassner, S. Walch and A.R. Winters. Entropy Stable Finite Volume Approximations for Ideal Magnetohydrodynamics. Jahresbericht der Deutschen Mathematiker-Vereinigung, Vol. 120: 153-219, 2018. |
| 43. | L. Friedrich, A.R. Winters, D.C. Del Rey Fernandez, G.J. Gassner, M. Parsani, M.H. Carpenter. An Entropy Stable h/p Non-Conforming Discontinuous Galerkin Method with the Summation-by-Parts Property. Journal of Scientific Computing, Vol. 77: 689-725, 2018. |
| 42. | D. Derigs, A.R. Winters, G.J. Gassner and S. Walch. Ideal GLM-MHD: About the entropy consistent nine-wave magnetic field divergence diminishing ideal magnetohydrodynamics equations. Journal of Computational Physics, Vol. 364: 420-467, 2018. |
| 41. | L. Friedrichs, D.C.D.R. Fernández, A R. Winters, G.J. Gassner, D.W. Zingg, and J. Hicken. Conservative and Stable Degree Preserving SBP Operators for Non-Conforming Meshes. Journal of Scientific Computing, Vol. 75: 657-686, 2018. |
| 40. | D. Flad, G.J. Gassner. On the use of kinetic energy preserving DG-schemes for large eddy simulation. Journal of Computational Physics, Vol. 350: 782-795. 2017. |
| 39. | N. Wintermeyer, A.R. Winters, G.J. Gassner, and D.A. Kopriva. An Entropy Stable Nodal Discontinuous Galerkin Method for the Two Dimensional Shallow Water Equations on Unstructured Curvilinear Meshes with Discontinuous Bathymetry. Journal of Computational Physics, Vol. 340: 200–242, 2017. |
| 38. | D.A. Kopriva, J. Nordström, G.J. Gassner. Error Boundedness of Discontinuous Galerkin Spectral Element Approximations of Hyperbolic Problems. Journal of Scientific Computing, Vol. 72: 314-330, 2017. |
| 37. | A.R. Winters, D. Derigs, G.J. Gassner and S. Walch. A Uniquely Defined Entropy Stable Matrix Dissipation Operator for High Mach Number Ideal MHD and Euler Simulations. Journal of Computational Physics, Vol. 332: 274–289, 2017. |
| 36. | D. Derigs, A.R. Winters, G.J. Gassner and S. Walch. A Novel Averaging Technique for Discrete Entropy-Stable Dissipation Operators for Ideal MHD. Journal of Computational Physics, Vol. 330: 624-632, 2017. |
| 35. | G.J. Gassner, A.R. Winters and D.A. Kopriva. Split Form Nodal Discontinuous Galerkin Schemes with Summation-By-Parts Property for the Compressible Euler Equations. Journal of Computational Physics, Vol. 327: 39-66, 2016. |
| 34. | D.A. Kopriva, A.R. Winters, M. Bohm, G.J. Gassner. A Provably Stable Discontinuous Galerkin Spectral Element Approximation for Moving Hexahedral Meshes. Computers & Fluids, Vol. 139: 148-160, 2016. |
| 33. | A.D. Beck, D.G. Flad, C. Tonhäuser, G.J. Gassner and C.-D. Munz On the Influence of Polynomial De-aliasing on Subgrid Scale Models. Flow, Turbulence and Combustion, Vol. 97: 475-511, 2016. |
| 32. | D. Derigs, A.R. Winters, G.J. Gassner and S. Walch. A Novel High-Order, Entropy Stable, 3D AMR MHD Solver with Guaranteed Positive Pressure. Journal of Computational Physics, Vol. 317: 223-256, 2016. |
| 31. | A.R. Winters and G.J. Gassner. Affordable, Entropy Conserving and Entropy Stable Flux Functions for the Ideal MHD Equations. Journal of Computational Physics, Vol. 304: 72–108, 2016. |
| 30. | D.A. Kopriva and G.J. Gassner. Geometry Effects in Nodal Discontinuous Galerkin Methods on Curved Elements that are Provably Stable. Applied Mathematics and Computation, Vol. 272(2): 274–290, 2016. |
| 29. | G.J. Gassner, A.R. Winters and D.A. Kopriva. A Well Balanced and Entropy Conservative Discontinuous Galerkin Spectral Element Method for the Shallow Water Equations. Applied Mathematics and Computation, Vol. 272(2): 291–308, 2016. |
| 28. | A.R. Winters and G.J. Gassner. A Comparison of Two Entropy Stable Discontinuous Galerkin Spectral Element Approximations for the Shallow Water Equations with Non-Constant Topography. Journal of Computational Physics, Vol. 301: 357–376, 2015. |
| 27. | A.R. Winters and G.J. Gassner. An Entropy Stable Finite Volume Scheme for the Equations of Shallow Water Magnetohydrodynamics. Journal of Scientific Computing, Vol. 301: 357-376, 2015. |
| 26. | G.J. Gassner, M. Staudenmaier, F. Hindenlang, M. Atak, C.-D. Munz. A Space-Time Adaptive Discontinuous Galerkin Scheme. Computers & Fluids, Vol. 117: 247–261, 2015. |
| 25. | Th. von Larcher, A. Beck, R. Klein, I. Horenko, P. Metzner, M. Waidmann, D. Igdalov, G. Gassner and C.-D. Munz. Towards a Framework for the Stochastic Modelling of Subgrid Scale Fluxes for Large Eddy Simulation. Meteorologische Zeitschrift, Vol. 24: 313-342, 2015. |
| 24. | D.A. Kopriva, G.J. Gassner. An Energy Stable Discontinuous Galerkin Spectral Element Discretization for Variable Coefficient Advection Problems. SIAM Journal of Scientific Computing, Vol. 36(4): A2076-A2099, 2014. |
| 23. | A.D. Beck, T. Bolemann, D. Flad, H. Frank, G.J. Gassner, F. Hindenlang, C.-D. Munz. High-order discontinuous Galerkin spectral element methods for transitional and turbulent flow simulations. International Journal for Numerical Methods in Fluids, Vol. 76: 522 - 548, 2014. |
| 22. | G.J. Gassner. A kinetic energy preserving nodal discontinuous Galerkin spectral element method. International Journal for Numerical Methods in Fluids, Vol. 76: 28-50, 2014. |
| 21. | F.J. Hindenlang, G.J. Gassner, C.-D. Munz. Improving the accuracy of discontinuous Galerkin schemes at boundary layers. International Journal for Numerical Methods in Fluids, Vol. 75: 385-402, 2014. |
| 20. | G. Gassner. A skew-symmetric discontinuous Galerkin spectral element discretization and its relation to SBP-SAT finite difference methods. SIAM Journal of Scientific Computing, Vol. 35: A1233-A1253, 2013. |
| 19. | P. Birken, G. Gassner, M. Haas, C.-D. Munz. Preconditioning for modal discontinuous Galerkin methods for unsteady 3D Navier-Stokes equations. Journal of Computational Physics, Vol. 240: 20-35, 2013. |
| 18. | J.P. Boyd, G. Gassner, Burhan A. Sadiq. The Nonconvergence of h-refinement in prolate elements. Journal of Scientific Computing, Vol. 57: 372-389, 2013. |
| 17. | G. Gassner. Dispersion and Dissipation Analysis of PNPM-schemes. Journal of Scientific Computing, Vol. 54: 21-44, 2013. |
| 16. | G.J. Gassner, A.D. Beck. On the Accuracy of High Order Discretizations for Underresolved Turbulence Simulations. Theoretical and Computational Fluid Dynamics, Vol. 27(3): 221-237, 2013. |
| 15. | A. Stock, J. Neudorfer, M. Riedlinger, G. Pirrung, G. Gassner, R. Schneider, S. Roller, C.-D. Munz. Three-Dimensional Numerical Simulation of a 30-GHz Gyrotron Resonator With an Explicit High-Order Discontinuous-Galerkin-Based Parallel Particle-In-Cell Method. IEEE Transactions on Plasma Science, Vol. 99: 1-11, 2012. |
| 14. | J. Neudorfer, A. Stock, J. Flamm, F. Hindenlang, G. Gassner, C.-D. Munz, R. Schneider, S. Roller Numerical Investigation of High-Order Gyrotron Mode Propagation in Launchers at 170 GHz. IEEE Transactions on Plasma Science, Vol. 40(6): 1512-1521, 2012. |
| 13. | F. Hindenlang, G. Gassner, C. Altmann, A. Beck, M. Staudenmaier, C.-D. Munz. Explicit Discontinuous Galerkin methods for unsteady problems. Computers&Fluids, Vol. 61: 86-93, 2012. |
| 12. | G. Gassner, D A. Kopriva. A Comparison of the Gauss and Gauss-Lobatto Discontinuous Galerkin Spectral Element Method for Wave Propagation Problems. SIAM Journal of Scientific Computing, Vol. 33(5): 2560-2576, 2011. |
| 11. | G. Gassner, M. Dumbser, F. Hindenlang, C.D. Munz. Explicit One-Step Time Discretizations for Discontinuous Galerkin and Finite Volume Schemes Based on Local Predictors. Journal of Computational Physics, Vol. 230(11): 4232-4247, 2011. |
| 10. | D.A. Kopriva, G. Gassner. On the Quadrature and Weak Form Choices in Collocation Type Discontinuous Galerkin Spectral Element Methods. Journal of Scientific Computing, Vol. 44(2): 136-155, 2010. |
| 9. | C. Altmann, G. Gassner, M. Staudenmaier, C.-D. Munz. High Order large Scale Calculations. inSiDE, Vol. 8(23): 12-15, 2010. |
| 8. | C. Altmann, G. Gassner, F. Lörcher, C.-D. Munz. A Space-Time Expansion Discontinuous Galerkin Scheme With Local Time Stepping for the Ideal and Viscous MHD Equations. IEEE Transactions on Plasma Science, Vol. (37): 513-519, 2009. |
| 7. | M. Dumbser, G. Gassner, C.-D. Munz. Discontinuous Galerkin-Verfahren für zeitabhängige Advektions-Diffusions-Gleichungen. Jahresbericht der Deutschen Mathematiker-Vereinigung Bd. 111 (2009). |
| 6. | G. Gassner, F. Lörcher, C.-D. Munz, J. S. Hesthaven. Polymorphic nodal elements and their application in discontinuous Galerkin methods. Journal of Computational Physics, Vol. (228): 1573-1590, 2009. |
| 5. | F. Lörcher, G. Gassner, C.-D. Munz. An explicit discontinuous Galerkin scheme with local time-stepping for general unsteady diffusion equations. Journal of Computational Physics, Vol. 227(11): 5649-5670, 2008. |
| 4. | G. Gassner, F. Lörcher, C.-D. Munz. A discontinuous Galerkin scheme based on a space-time expansion. II. Viscous flow equations in multi dimensions. J. Sci. Comp., Vol. 34(3): 260-286, 2008. |
| 3. | F. Lörcher, G. Gassner, C.-D. Munz. A discontinuous Galerkin scheme based on a space-time expansion. I. Inviscid compressible flow in one space dimension. J. Sci. Comp., Vol. 32(2): 175-199, 2007. |
| 2. | G. Gassner, F. Lörcher, C.-D. Munz. A contribution to the construction of diffusion fluxes for finite volume and discontinuous Galerkin schemes. Journal of Computational Physics, Vol. 224(2): 1049-1063, 2007. |
| 1. | B. Weigand, G. Gassner. The effect of wall conduction for the extended Graetz problem for laminar and turbulent flows. Int. J. Heat Mass Transfer, Vol. 50: 1097-1105, 2007. |