The mathematization of all sciences, the fading of traditional scientific boundaries, the
impact of computer technology, the growing importance of computer modelling and the …

Convection-diffusion-reaction equations model the conservation of scalar quantities. From
the analytic point of view, solutions of these equations satisfy, under certain conditions …

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 …

This work extends the flux-corrected transport (FCT) methodology to arbitrary order
continuous finite element discretizations of scalar conservation laws on simplex meshes …

We present a new perspective on the use of weighted essentially nonoscillatory (WENO)
reconstructions in high-order methods for scalar hyperbolic conservation laws. The main …

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 …

Recent results on the numerical analysis of algebraic flux correction (AFC) finite element
schemes for scalar convection–diffusion equations are reviewed and presented in a unified …

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 …