A contribution to the construction of diffusion fluxes for finite volume and discontinuous Galerkin schemes. - Gregor Gassner; Frieder Lörcher; Claus-Dieter Munz (J. Comput. Phys., 2007)

A Discontinuous Galerkin Scheme Based on a Space-Time Expansion. I. Inviscid Compressible Flow in One Space Dimension. - Frieder Lörcher; Gregor Gassner; Claus-Dieter Munz (J. Sci. Comput., 2007)

An explicit discontinuous Galerkin scheme with local time-stepping for general unsteady diffusion equations. - Frieder Lörcher; Gregor Gassner; Claus-Dieter Munz (J. Comput. Phys., 2008)

A Discontinuous Galerkin Scheme based on a Space-Time Expansion II. Viscous Flow Equations in Multi Dimensions. - Gregor Gassner; Frieder Lörcher; Claus-Dieter Munz (J. Sci. Comput., 2008)

Polymorphic nodal elements and their application in discontinuous Galerkin methods. - Gregor Gassner; Frieder Lörcher; Claus-Dieter Munz; Jan S. Hesthaven (J. Comput. Phys., 2009)

On the Quadrature and Weak Form Choices in Collocation Type Discontinuous Galerkin Spectral Element Methods. - David A. Kopriva; Gregor Gassner (J. Sci. Comput., 2010)

Discontinuous Galerkin for High Performance Computational Fluid Dynamics (hpcdg). - Christoph Altmann; Andrea Beck; Andreas Birkefeld; Florian Hindenlang; Marc Staudenmaier; Gregor Gassner; Claus-Dieter Munz (High Performance Computing in Science and Engineering, 2011)

Explicit one-step time discretizations for discontinuous Galerkin and finite volume schemes based on local predictors. - Gregor Gassner; Michael Dumbser; Florian Hindenlang; Claus-Dieter Munz (J. Comput. Phys., 2011)

A Comparison of the Dispersion and Dissipation Errors of Gauss and Gauss-Lobatto Discontinuous Galerkin Spectral Element Methods. - Gregor Gassner; David A. Kopriva (SIAM J. Sci. Comput., 2011)

An Efficient High Performance Parallelization of a Discontinuous Galerkin Spectral Element Method. - Christoph Altmann; Andrea D. Beck; Florian Hindenlang; Marc Staudenmaier; Gregor J. Gassner; Claus-Dieter Munz (Facing the Multicore-Challenge, 2012)

Discontinuous Galerkin for High Performance Computational Fluid Dynamics. - Andrea Beck; Thomas Bolemann; Hannes Frank; Florian Hindenlang; Marc Staudenmaier; Gregor Gassner; Claus-Dieter Munz (High Performance Computing in Science and Engineering, 2013)

Preconditioning for modal discontinuous Galerkin methods for unsteady 3D Navier-Stokes equations. - Philipp Birken; Gregor Gassner; Mark Haas; Claus-Dieter Munz (J. Comput. Phys., 2013)

The Nonconvergence of $$h$$ h -Refinement in Prolate Elements. - John P. Boyd 001; Gregor Gassner; Burhan A. Sadiq (J. Sci. Comput., 2013)

An Analysis of the Dissipation and Dispersion Errors of the P N P M Schemes. - Gregor Gassner (J. Sci. Comput., 2013)

A Skew-Symmetric Discontinuous Galerkin Spectral Element Discretization and Its Relation to SBP-SAT Finite Difference Methods. - Gregor Gassner (SIAM J. Sci. Comput., 2013)

An Energy Stable Discontinuous Galerkin Spectral Element Discretization for Variable Coefficient Advection Problems. - David A. Kopriva; Gregor Gassner (SIAM J. Sci. Comput., 2014)

A comparison of two entropy stable discontinuous Galerkin spectral element approximations for the shallow water equations with non-constant topography. - Andrew R. Winters; Gregor Gassner (J. Comput. Phys., 2015)

Preface to the special issue "Recent Advances in Numerical Methods for Hyperbolic Partial Differential Equations". - Michael Dumbser; Gregor Gassner; Christian Rohde; Sabine Roller (Appl. Math. Comput., 2016)

A well balanced and entropy conservative discontinuous Galerkin spectral element method for the shallow water equations. - Gregor Gassner; Andrew R. Winters; David A. Kopriva (Appl. Math. Comput., 2016)

Geometry effects in nodal discontinuous Galerkin methods on curved elements that are provably stable. - David A. Kopriva; Gregor Gassner (Appl. Math. Comput., 2016)

A novel high-order, entropy stable, 3D AMR MHD solver with guaranteed positive pressure. - Dominik Derigs; Andrew R. Winters; Gregor J. Gassner; Stefanie Walch (J. Comput. Phys., 2016)

Split form nodal discontinuous Galerkin schemes with summation-by-parts property for the compressible Euler equations. - Gregor J. Gassner; Andrew R. Winters; David A. Kopriva (J. Comput. Phys., 2016)

Affordable, entropy conserving and entropy stable flux functions for the ideal MHD equations. - Andrew R. Winters; Gregor J. Gassner (J. Comput. Phys., 2016)

An Entropy Stable Finite Volume Scheme for the Equations of Shallow Water Magnetohydrodynamics. - Andrew R. Winters; Gregor J. Gassner (J. Sci. Comput., 2016)

A novel averaging technique for discrete entropy-stable dissipation operators for ideal MHD. - Dominik Derigs; Andrew R. Winters; Gregor J. Gassner; Stefanie Walch (J. Comput. Phys., 2017)

On the use of kinetic energy preserving DG-schemes for large eddy simulation. - David Flad; Gregor Gassner (J. Comput. Phys., 2017)

An entropy stable nodal discontinuous Galerkin method for the two dimensional shallow water equations on unstructured curvilinear meshes with discontinuous bathymetry. - Niklas Wintermeyer; Andrew R. Winters; Gregor J. Gassner; David A. Kopriva (J. Comput. Phys., 2017)

A uniquely defined entropy stable matrix dissipation operator for high Mach number ideal MHD and compressible Euler simulations. - Andrew R. Winters; Dominik Derigs; Gregor J. Gassner; Stefanie Walch (J. Comput. Phys., 2017)

Error Boundedness of Discontinuous Galerkin Spectral Element Approximations of Hyperbolic Problems. - David A. Kopriva; Jan Nordström; Gregor J. Gassner (J. Sci. Comput., 2017)

Ideal GLM-MHD: About the entropy consistent nine-wave magnetic field divergence diminishing ideal magnetohydrodynamics equations. - Dominik Derigs; Andrew R. Winters; Gregor J. Gassner; Stefanie Walch; Marvin Bohm (J. Comput. Phys., 2018)

An entropy stable discontinuous Galerkin method for the shallow water equations on curvilinear meshes with wet/dry fronts accelerated by GPUs. - Niklas Wintermeyer; Andrew R. Winters; Gregor J. Gassner; Timothy Warburton (J. Comput. Phys., 2018)

A comparative study on polynomial dealiasing and split form discontinuous Galerkin schemes for under-resolved turbulence computations. - Andrew R. Winters; Rodrigo Costa Moura; Gianmarco Mengaldo; Gregor J. Gassner; Stefanie Walch; Joaquim Peiró; Spencer J. Sherwin (J. Comput. Phys., 2018)

Conservative and Stable Degree Preserving SBP Operators for Non-conforming Meshes. - Lucas Friedrich; David C. Del Rey Fernández; Andrew R. Winters; Gregor J. Gassner; David W. Zingg; Jason E. Hicken (J. Sci. Comput., 2018)

An Entropy Stable h / p Non-Conforming Discontinuous Galerkin Method with the Summation-by-Parts Property. - Lucas Friedrich; Andrew R. Winters; David C. Del Rey Fernández; Gregor J. Gassner; Matteo Parsani; Mark H. Carpenter (J. Sci. Comput., 2018)

The BR1 Scheme is Stable for the Compressible Navier-Stokes Equations. - Gregor J. Gassner; Andrew R. Winters; Florian Hindenlang; David A. Kopriva (J. Sci. Comput., 2018)

Correction to: The BR1 Scheme is Stable for the Compressible Navier-Stokes Equations. - Gregor J. Gassner; Andrew R. Winters; Florian Hindenlang; David A. Kopriva (J. Sci. Comput., 2018)

Entropy stable numerical approximations for the isothermal and polytropic Euler equations. - Andrew R. Winters; Christof Czernik; Moritz B. Schily; Gregor J. Gassner (CoRR, 2019)

Entropy Stable p-Nonconforming Discretizations with the Summation-by-Parts Property for the Compressible Euler equations. - David C. Del Rey Fernández; Mark H. Carpenter; Lisandro Dalcín; L. Fredrich; Diego Rojas; Andrew R. Winters; Gregor J. Gassner; Stefano Zampini; Matteo Parsani (CoRR, 2019)

Entropy Stable p-Nonconforming Discretizations with the Summation-by-Parts Property for the Compressible Navier-Stokes Equations. - David C. Del Rey Fernández; Mark H. Carpenter; Lisandro Dalcín; Lucas Friedrich; Andrew R. Winters; Gregor J. Gassner; Matteo Parsani (CoRR, 2019)

Multi-element SIAC Filter for Shock Capturing Applied to High-Order Discontinuous Galerkin Spectral Element Methods. - Marvin Bohm; Sven Schermeng; Andrew R. Winters; Gregor J. Gassner; Gustaaf B. Jacobs (J. Sci. Comput., 2019)

Entropy Stable Space-Time Discontinuous Galerkin Schemes with Summation-by-Parts Property for Hyperbolic Conservation Laws. - Lucas Friedrich; Gero Schnücke; Andrew R. Winters; David C. Del Rey Fernández; Gregor J. Gassner; Mark H. Carpenter (J. Sci. Comput., 2019)

Free-Stream Preservation for Curved Geometrically Non-conforming Discontinuous Galerkin Spectral Elements. - David A. Kopriva; Florian Hindenlang; Thomas Bolemann; Gregor J. Gassner (J. Sci. Comput., 2019)

Construction of Modern Robust Nodal Discontinuous Galerkin Spectral Element Methods for the Compressible Navier-Stokes Equations. - Andrew R. Winters; David A. Kopriva; Gregor J. Gassner; Florian Hindenlang (CoRR, 2020)

Preventing pressure oscillations does not fix local linear stability issues of entropy-based split-form high-order schemes. - Hendrik Ranocha; Gregor J. Gassner (CoRR, 2020)

A Sub-Element Adaptive Shock Capturing Approach for Discontinuous Galerkin Methods. - Johannes Markert; Gregor Gassner; Stefanie Walch (CoRR, 2020)

An entropy stable nodal discontinuous Galerkin method for the resistive MHD equations. Part I: Theory and numerical verification. - Marvin Bohm; Andrew R. Winters; Gregor J. Gassner; Dominik Derigs; Florian Hindenlang; Joachim Saur (J. Comput. Phys., 2020)

Split form ALE discontinuous Galerkin methods with applications to under-resolved turbulent low-Mach number flows. - Nico Krais; Gero Schnücke; Thomas Bolemann; Gregor J. Gassner (J. Comput. Phys., 2020)

Entropy Stable Discontinuous Galerkin Schemes on Moving Meshes for Hyperbolic Conservation Laws. - Gero Schnücke; Nico Krais; Thomas Bolemann; Gregor J. Gassner (J. Sci. Comput., 2020)

FLEXI: A high order discontinuous Galerkin framework for hyperbolic-parabolic conservation laws. - Nico Krais; Andrea Beck; Thomas Bolemann; Hannes Frank; David Flad; Gregor Gassner; Florian Hindenlang; Malte Hoffmann; Thomas Kuhn; Matthias Sonntag; Claus-Dieter Munz (Comput. Math. Appl., 2021)

A Subcell Finite Volume Positivity-Preserving Limiter for DGSEM Discretizations of the Euler Equations. - Andrés M. Rueda-Ramírez; Gregor J. Gassner (CoRR, 2021)

Adaptive numerical simulations with Trixi.jl: A case study of Julia for scientific computing. - Hendrik Ranocha; Michael Schlottke-Lakemper; Andrew R. Winters; Erik Faulhaber; Jesse Chan; Gregor J. Gassner (CoRR, 2021)

Local Fourier Analysis of a Space-Time Multigrid Method for DG-SEM for the Linear Advection Equation. - Lea M. Versbach; Philipp Birken; Viktor Linders; Gregor Gassner (CoRR, 2021)

A Discontinuous Galerkin Solver in the FLASH Multi-Physics Framework. - Johannes Markert; Stefanie Walch; Gregor Gassner (CoRR, 2021)

A provably entropy stable subcell shock capturing approach for high order split form DG for the compressible Euler equations. - Sebastian Hennemann; Andrés M. Rueda-Ramírez; Florian J. Hindenlang; Gregor J. Gassner (J. Comput. Phys., 2021)

An entropy stable nodal discontinuous Galerkin method for the resistive MHD equations. Part II: Subcell finite volume shock capturing. - Andrés M. Rueda-Ramírez; Sebastian Hennemann; Florian J. Hindenlang; Andrew R. Winters; Gregor J. Gassner (J. Comput. Phys., 2021)

A purely hyperbolic discontinuous Galerkin approach for self-gravitating gas dynamics. - Michael Schlottke-Lakemper; Andrew R. Winters; Hendrik Ranocha; Gregor J. Gassner (J. Comput. Phys., 2021)

A Split-form, Stable CG/DG-SEM for Wave Propagation Modeled by Linear Hyperbolic Systems. - David A. Kopriva; Gregor J. Gassner (J. Sci. Comput., 2021)

Stability of Discontinuous Galerkin Spectral Element Schemes for Wave Propagation when the Coefficient Matrices have Jumps. - David A. Kopriva; Gregor J. Gassner; Jan Nordström (J. Sci. Comput., 2021)

Subcell limiting strategies for discontinuous Galerkin spectral element methods. - Andrés M. Rueda-Ramírez; Will Pazner; Gregor J. Gassner (CoRR, 2022)

On the entropy projection and the robustness of high order entropy stable discontinuous Galerkin schemes for under-resolved flows. - Jesse Chan; Hendrik Ranocha; Andrés M. Rueda-Ramírez; Gregor Gassner; Tim Warburton (CoRR, 2022)

On error-based step size control for discontinuous Galerkin methods for compressible fluid dynamics. - Hendrik Ranocha; Andrew R. Winters; Hugo Guillermo Castro; Lisandro Dalcín; Michael Schlottke-Lakemper; Gregor J. Gassner; Matteo Parsani (CoRR, 2022)

On the theoretical foundation of overset grid methods for hyperbolic problems II: Entropy bounded formulations for nonlinear conservation laws. - David A. Kopriva; Gregor J. Gassner; Jan Nordström (J. Comput. Phys., 2022)

On the theoretical foundation of overset grid methods for hyperbolic problems: Well-posedness and conservation. - David A. Kopriva; Jan Nordström; Gregor J. Gassner (J. Comput. Phys., 2022)

Stability Issues of Entropy-Stable and/or Split-form High-order Schemes. - Gregor J. Gassner; Magnus Svärd; Florian J. Hindenlang (J. Sci. Comput., 2022)

Monolithic Convex Limiting for Legendre-Gauss-Lobatto Discontinuous Galerkin Spectral Element Methods. - Andrés M. Rueda-Ramírez; Benjamin Bolm; Dmitri Kuzmin; Gregor J. Gassner (CoRR, 2023)

High-order upwind summation-by-parts methods for nonlinear conservation laws. - Hendrik Ranocha; Andrew R. Winters; Michael Schlottke-Lakemper; Philipp Öffner; Jan Glaubitz; Gregor J. Gassner (CoRR, 2023)

Entropy-stable Gauss collocation methods for ideal magneto-hydrodynamics. - Andrés M. Rueda-Ramírez; Florian J. Hindenlang; Jesse Chan; Gregor J. Gassner (J. Comput. Phys., 2023)

Spatial discontinuous Galerkin spectral element method for a family of chromatography models in CADET. - Jan Michael Breuer; Samuel Leweke; Johannes Schmölder; Gregor Gassner; Eric von Lieres (Comput. Chem. Eng., 2023)

Efficient Implementation of Modern Entropy Stable and Kinetic Energy Preserving Discontinuous Galerkin Methods for Conservation Laws. - Hendrik Ranocha; Michael Schlottke-Lakemper; Jesse Chan; Andrés M. Rueda-Ramírez; Andrew R. Winters; Florian Hindenlang; Gregor J. Gassner (ACM Trans. Math. Softw., 2023)

Lossy Data Compression By Adaptive Mesh Coarsening. - Niklas Böing; Johannes Holke; Chiara Hergl; Luca Spataro; Gregor Gassner; Achim Basermann (CoRR, 2024)

Fourth-Order Paired-Explicit Runge-Kutta Methods. - Daniel Doehring; Lars Christmann; Michael Schlottke-Lakemper; Gregor J. Gassner; Manuel Torrilhon (CoRR, 2024)

Mimetic Metrics for the DGSEM. - Daniel Bach; Andrés M. Rueda-Ramírez; David A. Kopriva; Gregor J. Gassner (CoRR, 2024)

Multirate time-integration based on dynamic ODE partitioning through adaptively refined meshes for compressible fluid dynamics. - Daniel Doehring; Michael Schlottke-Lakemper; Gregor J. Gassner; Manuel Torrilhon (J. Comput. Phys., 2024)

A flux-differencing formula for split-form summation by parts discretizations of non-conservative systems: Applications to subcell limiting for magneto-hydrodynamics. - Andrés M. Rueda-Ramírez; Gregor J. Gassner (J. Comput. Phys., 2024)

Many-Stage Optimal Stabilized Runge-Kutta Methods for Hyperbolic Partial Differential Equations. - Daniel Doehring; Gregor J. Gassner; Manuel Torrilhon (J. Sci. Comput., 2024)

Generalized upwind summation-by-parts operators and their application to nodal discontinuous Galerkin methods. - Jan Glaubitz; Hendrik Ranocha; Andrew R. Winters; Michael Schlottke-Lakemper; Philipp Öffner; Gregor Gassner (J. Comput. Phys., 2025)

On the robustness of high-order upwind summation-by-parts methods for nonlinear conservation laws. - Hendrik Ranocha; Andrew R. Winters; Michael Schlottke-Lakemper; Philipp Öffner; Jan Glaubitz; Gregor J. Gassner (J. Comput. Phys., 2025)

An entropy-stable discontinuous Galerkin discretization of the ideal multi-ion magnetohydrodynamics system. - Andrés M. Rueda-Ramírez; Aleksey Sikstel; Gregor J. Gassner (J. Comput. Phys., 2025)

TrixiParticles.jl: Particle-based multiphysics simulation in Julia. - Niklas S. Neher; Erik Faulhaber; Sven Berger; Gregor J. Gassner; Michael Schlottke-Lakemper (J. Open Source Softw., 2025)

Robust and efficient pre-processing techniques for particle-based methods including dynamic boundary generation. - Niklas S. Neher; Erik Faulhaber; Sven Berger; Christian Weißenfels; Gregor J. Gassner; Michael Schlottke-Lakemper (CoRR, 2025)