A posteriori subcell limiting of the discontinuous Galerkin finite element method for hyperbolic conservation laws
M Dumbser, O Zanotti, R Loubère, S Diot - Journal of Computational …, 2014 - Elsevier
The purpose of this work is to propose a novel a posteriori finite volume subcell limiter
technique for the Discontinuous Galerkin finite element method for nonlinear systems of …
technique for the Discontinuous Galerkin finite element method for nonlinear systems of …
[HTML][HTML] High order ADER schemes for a unified first order hyperbolic formulation of continuum mechanics: viscous heat-conducting fluids and elastic solids
This paper is concerned with the numerical solution of the unified first order hyperbolic
formulation of continuum mechanics recently proposed by Peshkov and Romenski [110] …
formulation of continuum mechanics recently proposed by Peshkov and Romenski [110] …
Space–time adaptive ADER discontinuous Galerkin finite element schemes with a posteriori sub-cell finite volume limiting
In this paper we present a novel arbitrary high order accurate discontinuous Galerkin (DG)
finite element method on space–time adaptive Cartesian meshes (AMR) for hyperbolic …
finite element method on space–time adaptive Cartesian meshes (AMR) for hyperbolic …
[HTML][HTML] A simple robust and accurate a posteriori sub-cell finite volume limiter for the discontinuous Galerkin method on unstructured meshes
M Dumbser, R Loubère - Journal of Computational Physics, 2016 - Elsevier
In this paper we propose a simple, robust and accurate nonlinear a posteriori stabilization of
the Discontinuous Galerkin (DG) finite element method for the solution of nonlinear …
the Discontinuous Galerkin (DG) finite element method for the solution of nonlinear …
ADER-WENO finite volume schemes with space–time adaptive mesh refinement
We present the first high order one-step ADER-WENO finite volume scheme with adaptive
mesh refinement (AMR) in multiple space dimensions. High order spatial accuracy is …
mesh refinement (AMR) in multiple space dimensions. High order spatial accuracy is …
[HTML][HTML] ExaHyPE: An engine for parallel dynamically adaptive simulations of wave problems
Abstract ExaHyPE (“An Exascale Hyperbolic PDE Engine”) is a software engine for solving
systems of first-order hyperbolic partial differential equations (PDEs). Hyperbolic PDEs are …
systems of first-order hyperbolic partial differential equations (PDEs). Hyperbolic PDEs are …
High order ADER schemes for continuum mechanics
In this paper we first review the development of high order ADER finite volume and ADER
discontinuous Galerkin schemes on fixed and moving meshes, since their introduction in …
discontinuous Galerkin schemes on fixed and moving meshes, since their introduction in …
Linearly implicit Rosenbrock-type Runge–Kutta schemes applied to the Discontinuous Galerkin solution of compressible and incompressible unsteady flows
In this work we investigate the use of linearly implicit Rosenbrock-type Runge–Kutta
schemes to integrate in time high-order Discontinuous Galerkin space discretizations of the …
schemes to integrate in time high-order Discontinuous Galerkin space discretizations of the …
ADER discontinuous Galerkin schemes for general-relativistic ideal magnetohydrodynamics
We present a new class of high-order accurate numerical algorithms for solving the
equations of general-relativistic ideal magnetohydrodynamics in curved space–times. In this …
equations of general-relativistic ideal magnetohydrodynamics in curved space–times. In this …
A new family of high order unstructured MOOD and ADER finite volume schemes for multidimensional systems of hyperbolic conservation laws
R Loubere, M Dumbser, S Diot - Communications in Computational …, 2014 - cambridge.org
In this paper, we investigate the coupling of the Multi-dimensional Optimal Order Detection
(MOOD) method and the Arbitrary high order DERivatives (ADER) approach in order to …
(MOOD) method and the Arbitrary high order DERivatives (ADER) approach in order to …