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 …

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 …

We propose a new pressure-based structure-preserving (SP) and quasi asymptotic
preserving (AP) staggered semi-implicit finite volume scheme for the unified first order …

In this paper we discuss a new and very efficient implementation of high order accurate
arbitrary high order schemes using derivatives discontinuous Galerkin (ADER-DG) finite …

Earthquake fault zones are more complex, both geometrically and rheologically, than an
idealized infinitely thin plane embedded in linear elastic material. To incorporate nonlinear …

A high-order accurate implicit-mesh discontinuous Galerkin framework for wave propagation
in single-phase and bi-phase solids is presented. The framework belongs to the embedded …

We discuss the applicability of a unified hyperbolic model for continuum fluid and solid
mechanics to modeling non-Newtonian flows and in particular to modeling the stress-driven …

A cell-centered implicit-explicit updated Lagrangian finite volume scheme on unstructured
grids is proposed for a unified first-order hyperbolic formulation of continuum fluid and solid …

We are concerned with the numerical solution of a unified first order hyperbolic formulation
of continuum mechanics that goes back to the work of Godunov, Peshkov and Romenski …

In this paper we propose a new diffuse interface model for the numerical simulation of
inviscid compressible flows around fixed and moving solid bodies of arbitrary shape. The …