356 citations · 4.2k across the 89 of their papers we have counts for
98 papers
ADER-ZIST - a mixed explicit ADER-DG and zonally implicit space-time DG approach for Cartesian cut cell meshes
Michael Dumbser, Christian Engwer, Sandra May +1
We present high order accurate mixed explicit-implicit discontinuous Galerkin (DG) schemes for the solution of hyperbolic systems of conservation laws on Cartesian cut cell meshes.…
An arbitrarily high-order accurate and locally energy/entropy-stable space-time method for a class of nonlinear wave systems
Michael Dumbser, Ilaria Perugia, Enrico Zampa
We present a new class of structure-preserving, arbitrarily high-order accurate space-time schemes using unstructured simplicial meshes in space for a class of nonlinear acoustic w…
On structure-preserving and pointwise conservative continuous DG schemes for hyperbolic systems
Rémi Abgrall, Michael Dumbser, Pierre-Henri Maire +1
We present a new class of structure-preserving semi-discrete continuous-discontinuous Galerkin (CG-DG) finite element schemes for linear and nonlinear hyperbolic systems of partial…
A structure-preserving semi-implicit finite volume scheme on vertex-staggered unstructured meshes
Elena Bernardelli, Elena Gaburro, Michael Dumbser
We present a novel structure-preserving semi-implicit finite volume method on vertex-based staggered meshes for the compatible discretization of first order systems of time-depende…
On general and complete multidimensional Riemann solvers for nonlinear systems of hyperbolic conservation laws
Elena Gaburro, Mario Ricchiuto, Michael Dumbser
In this work, we introduce a framework to design multidimensional Riemann solvers for nonlinear systems of hyperbolic conservation laws on general unstructured polygonal Voronoi-li…
A simple and general framework for the construction of exactly div-curl-grad compatible discontinuous Galerkin finite element schemes on unstructured simplex meshes
R. Abgrall, M. Dumbser, P. H. Maire
We introduce a new family of discontinuous Galerkin (DG) finite element schemes for the discretization of first order systems of hyperbolic partial differential equations (PDE) on…