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

The contents of this paper is twofold. First, important recent results concerning finite element
methods for convection-dominated problems and incompressible flow problems are …

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 …

Simplicial Partitions with Applications to the Finite Element Method Page 1 Springer
Monographs in Mathematics Simplicial Partitions with Applications to the Finite Element …

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 …

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 …

For the case of approximation of convection–diffusion equations using piecewise affine
continuous finite elements a new edge-based nonlinear diffusion operator is proposed that …

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

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 …

In the field of computational fluid dynamics, many applications of practical interest require
the use of robust discretization techniques equipped with adaptive control mechanisms for …