Publications

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.