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 …

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 …

In this work we present a framework for enforcing discrete maximum principles in
discontinuous Galerkin (DG) discretizations. The developed schemes are applicable to …

Many mathematical models of continuum mechanics are derived from integral conservation
laws. Examples of such models include the Euler and Navier–Stokes equations of fluid …

In this paper, we propose a family of second and third order temporal integration methods for
systems of stiff ordinary differential equations, and explore their application in solving the …

We demonstrate that the streamline‐upwind/Petrov–Galerkin (SUPG) formulation enhanced
with YZβ discontinuity‐capturing, that is, the SUPG‐YZβ formulation, is an efficient and …

When adopting high-order finite volume schemes based on MUSCL reconstruction
techniques to approximate the weak solutions of hyperbolic systems with source terms, the …

Multiwavelets (MW) enable the compression, analysis and assembly of model data on a
multiresolution grid within Godunov-type solvers based on second-order discontinuous …

This work introduces a new type of constrained algebraic stabilization for continuous
piecewise-linear finite element approximations to the equations of ideal …