We present a new family of very high order accurate direct Arbitrary-Lagrangian-Eulerian
(ALE) Finite Volume (FV) and Discontinuous Galerkin (DG) schemes for the solution of …

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 …

Solutions to many partial differential equations satisfy certain bounds or constraints. For
example, the density and pressure are positive for equations of fluid dynamics, and in the …

We introduce an approximation technique for nonlinear hyperbolic systems with sources that
is invariant domain preserving. The method is discretization-independent provided …

This book is the third volume of a three-part textbook suitable for graduate coursework,
professional engineering and academic research. It is also appropriate for graduate flipped …

We present a fully discrete approximation technique for the compressible Navier–Stokes
equations that is second-order accurate in time and space, semi-implicit, and guaranteed to …

In this paper, we develop high-order nodal discontinuous Galerkin (DG) methods for
hyperbolic conservation laws that satisfy invariant domain preserving properties using …

Using the theoretical framework of algebraic flux correction and invariant domain preserving
schemes, we introduce a monolithic approach to convex limiting in continuous finite element …

The algebraic flux correction (AFC) schemes presented in this work constrain a standard
continuous finite element discretization of a nonlinear hyperbolic problem to satisfy relevant …

This paper proposes an invariant-domain preserving approximation technique for nonlinear
conservation systems that is high-order accurate in space and time. The algorithm mixes a …