For highly coupled nonlinear incompressible magnetohydrodynamic (MHD) system, a well-
known numerical challenge is how to establish an unconditionally energy stable linearized …

Many mathematical models of continuum mechanics are derived from integral conservation
laws. Examples of such models include the Euler and Navier–Stokes equations of fluid …

We present a novel high-order nodal artificial viscosity approach designed for solving
Magnetohydrodynamics (MHD) equations. Unlike conventional methods, our approach …

We present a high order, robust, and stable shock-capturing technique for finite element
approximations of ideal MHD. The method uses continuous Lagrange polynomials in space …

This study considers an implicit finite element formulation for an ideal fully-ionized multifluid
electromagnetic plasma system. The formulation is based on fully-implicit Runge-Kutta time …

We show at the PDE level that the monolithic parabolic regularization of the equations of
ideal magnetohydrodynamics (MHD) is compatible with all the generalized entropies, fulfills …

We introduce a new hybridized discontinuous Galerkin method for the incompressible
magnetohydrodynamics equations. If particular velocity, pressure, magnetic field, and …

When the magnetic Reynolds number R em≪ 1, the induced magnetic field caused by the
applied electric field E 0 and the applied magnetic field B 0 can be neglected for …

Nonlinear conservation laws such as the system of ideal magnetohydrodynamics (MHD)
equations may develop singularities over time. In these situations, viscous regularization is a …

By combination of iteration methods with the partition of unity method (PUM), some finite
element parallel algorithms for the stationary incompressible magnetohydrodynamics (MHD) …