The rotating shallow water (RSW) equations are the usual testbed for the development of
numerical methods for three-dimensional atmospheric and oceanic models. However, an …

We propose a finite-element discretization approach for the incompressible Euler equations
which mimics their geometric structure and their variational derivation. In particular, we …

We introduce a novel structure-preserving method in order to approximate the compressible
ideal Magnetohydrodynamics (MHD) equations. This technique addresses the MHD …

Convection-diffusion equations arise in a variety of applications such as particle transport,
electromagnetics, and magnetohydrodynamics. Simulation of the convection-dominated …

We propose and analyze a hybridizable discontinuous Galerkin (HDG) method for solving a
mixed magnetic advection–diffusion problem within a more general Friedrichs system …

This paper is devoted to the construction and analysis of the finite element approximations
for the H(D) convection-diffusion problems, where D can be chosen as grad, curl, or div in …

We devise and analyze a class of the primal discontinuous Galerkin methods for the
magnetic advection-diffusion problems based on the weighted-residual approach. In …

The equations of magnetohydrodynamics (MHD) model the interaction of conducting fluids
with electromagnetic fields, and provide the mathematical description of problems arising in …

We present a novel asymptotic-preserving semi-implicit finite element method for weakly
compressible and incompressible flows based on compatible finite element spaces. The …

We devise and analyze an edge-based scheme on polyhedral meshes to approximate a
vector advection-reaction problem. The well-posedness of the discrete problem is analyzed …