5 papers
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…
Dual Formulation Finite-Volume Methods on Overlapping Meshes for Hyperbolic Conservation Laws
Rémi Abgrall, Alina Chertock, Alexander Kurganov +1
In this work, we introduce new second-order schemes for one- and two-dimensional hyperbolic systems of conservation laws. Following an approach recently proposed in [{\sc R. Abgral…
Embedding General Conservation Constraints in Discretizations of Hyperbolic Systems on Arbitrary Meshes: A Multidimensional Framework
Rémi Abgrall, Pierre-Henri Maire, Mario Ricchiuto
The purpose of this review is to discuss the notion of conservation in hyperbolic systems and how one can formulate it at the discrete level depending on the solution representatio…
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…
A semi-discrete Active Flux method for the Euler equations on Cartesian grids
Rémi Abgrall, Wasilij Barsukow, Christian Klingenberg
Active Flux is an extension of the Finite Volume method and additionally incorporates point values located at cell boundaries. This gives rise to a globally continuous approximatio…