We develop a semi-Lagrangian discretization of the time-dependent incompressible Navier-
Stokes equations with free boundary conditions on arbitrary simplicial meshes. We recast …

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 deal with the discretization of generalized transient advection problems for differential
forms on bounded spatial domains. We pursue an Eulerian method of lines approach with …

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

We start from the splitting of the equations of single-fluid magnetohydrodynamics (MHD) into
a magnetic induction part and a fluid part. We design novel numerical methods for the MHD …

Many computational problems incorporate discontinuities that evolve in time. The
eXtendend Finite Element Method (XFEM) is able to represent discontinuities sharply on …

This paper presents a novel approach to the construction of the lowest order $ H (\mathrm
{curl}) $ and $ H (\mathrm {div}) $ exponentially-fitted finite element spaces ${\mathcal {S} …

A perturbed black hole produces characteristic radiations whose frequencies possess some
physical information of the black hole such as its mass and angular momentum. We have …

Stabilized Galerkin for Linear Advection of Vector Fields Page 1 Stabilized Galerkin for
Linear Advection of Vector Fields Holger Heumann and Ralf Hiptmair Abstract We present a …

Here, A stands a magnetic vector potential arising from temporal gauge, js is a source
current and Rm is the so-called magnetic Reynolds number, which indicates the relative …