A new second-order method for approximating the compressible Euler equations is
introduced. The method preserves all the known invariant domains of the Euler system …

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 …

In this article, we motivate, derive, and test effective preconditioners to be used with the
Minres algorithm for solving a number of saddle point systems which arise in PDE …

This paper proposes an explicit,(at least) second-order, maximum principle satisfying,
Lagrange finite element method for solving nonlinear scalar conservation equations. The …

We present a new spectral framework to design and optimise numerical methods for
convection problems termed Local Transfer function Analysis (LTA), which improves the …

When integrating unsteady problems using globally continuous representation of the
solution, as for continuous finite element methods, one faces the problem of inverting a mass …

We propose a technique for approximating nonlinear scalar conservation equations that
uses continuous finite elements and is formally (at least) second-order accurate in space …

In this work, we propose a nonlinear stabilization technique for scalar conservation laws with
implicit time stepping. The method relies on an artificial diffusion method, based on a graph …

This paper introduces a first-order viscosity method for the explicit approximation of scalar
conservation equations with Lipschitz fluxes using continuous finite elements on arbitrary …