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06/22/2023
An entropy stable discontinuous Galerkin method for the two-layer shallow water equations on curvilinear meshes
We present an entropy stable nodal discontinuous Galerkin spectral eleme...
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09/15/2022
On error-based step size control for discontinuous Galerkin methods for compressible fluid dynamics
We study temporal step size control of explicit Runge-Kutta methods for ...
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12/20/2021
Efficient implementation of modern entropy stable and kinetic energy preserving discontinuous Galerkin methods for conservation laws
Many modern discontinuous Galerkin (DG) methods for conservation laws ma...
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08/14/2021
Adaptive numerical simulations with Trixi.jl: A case study of Julia for scientific computing
We present Trixi.jl, a Julia package for adaptive high-order numerical s...
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12/22/2020
An Entropy Stable Nodal Discontinuous Galerkin Method for the resistive MHD Equations. Part II: Subcell Finite Volume Shock Capturing
The second paper of this series presents two robust entropy stable shock...
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08/24/2020
A purely hyperbolic discontinuous Galerkin approach for self-gravitating gas dynamics
One of the challenges when simulating astrophysical flows with self-grav...
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07/14/2020
Stable filtering procedures for nodal discontinuous Galerkin methods
We prove that the most common filtering procedure for nodal discontinuou...
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05/05/2020
Construction of Modern Robust Nodal Discontinuous Galerkin Spectral Element Methods for the Compressible Navier-Stokes Equations
Discontinuous Galerkin (DG) methods have a long history in computational...
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09/27/2019
Entropy Stable p-Nonconforming Discretizations with the Summation-by-Parts Property for the Compressible Navier-Stokes Equations
The entropy conservative, curvilinear, nonconforming, p-refinement algor...
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07/24/2019
Energy versus entropy estimates for nonlinear hyperbolic systems of equations
We compare and contrast information provided by the energy analysis of K...
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07/10/2019
Multi-element SIAC filter for shock capturing applied to high-order discontinuous Galerkin spectral element methods
We build a multi-element variant of the smoothness increasing accuracy c...
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07/07/2019
