The magnetohydrodynamics (MHD) equations are generally known to be difficult to solve
numerically, due to their highly nonlinear structure and the strong coupling between the …

Obtaining a satisfactory numerical solution of the classical three-dimensional drift-diffusion
(DD) model, widely used in semiconductor device simulations, is still challenging nowadays …

We develop a theory of finite element systems, for the purpose of discretizing sections of
vector bundles, in particular those arising in the theory of elasticity. In the presence of …

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

Scalar convection-diffusion has been drawing attention in fluid mechanics since more than
half a century due to its relevance in various applications, its impact on transport properties …

This work proposes a new stabilized P 1× P 0 finite element method for solving the
incompressible Navier–Stokes equations. The numerical scheme is based on a reduced …

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

The moving mesh method is one of the important adaptive mesh methods which is
practically useful when the mesh size and overall resolution are provided and fixed as seen …

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

We present compatible finite element space discretizations for the ideal compressible
magnetohydrodynamic equations. The magnetic field is considered both in div-and curl …