21 citations · 25 across the 4 of their papers we have counts for
7 papers · 1 filter
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…
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 structure-preserving and thermodynamically compatible cell-centered Lagrangian finite volume scheme for continuum mechanics
Walter Boscheri, Michael Dumbser, Raphael Loubère +1
In this work we present a novel structure-preserving scheme for the discretization of the Godunov-Peshkov-Romenski (GPR) model of continuum mechanics written in Lagrangian form. Th…
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 node-conservative vorticity-preserving Finite Volume method for linear acoustics on unstructured grids
Wasilij Barsukow, Raphaël Loubère, Pierre-Henri Maire
Instead of ensuring that fluxes across edges add up to zero, we split the edge in two halves and also associate different fluxes to each of its sides. This is possible due to non-s…
A geometrically and thermodynamically compatible finite volume scheme for continuum mechanics on unstructured polygonal meshes
Walter Boscheri, Raphael Loubére, Jean-Philippe Braeunig +1
We present a novel Finite Volume (FV) scheme on unstructured polygonal meshes that is provably compliant with the Second Law of Thermodynamics and the Geometric Conservation Law (G…