In this paper, we consider numerical approximations for the viscous Cahn–Hilliard equation
with hyperbolic relaxation. This type of equations processes energy-dissipative structure …

We consider numerical approximations for a phase field dendritic crystal growth model,
which is a highly nonlinear system that couples the anisotropic Allen–Cahn type equation …

In the numerical simulation of ideal magnetohydrodynamics (MHD), keeping the pressure
and density always positive is essential for both physical considerations and numerical …

In this paper, we consider numerical approximations for the anisotropic Cahn–Hilliard
equation. We develop two linear and second-order schemes that combine the IEQ approach …

In this paper, we consider numerical approximations for solving the magneto-hydrodynamic
equations, which couples the Navier–Stokes equations and Maxwell equations together. A …

An efficient element-free Galerkin (EFG) method is developed to solve Signorini boundary
value problems. The nonlinear inequality Signorini boundary conditions are reduced to a …

In this paper, we develop two second-order in time, linear and unconditionally energy stable
time marching schemes for solving the nonlocal Cahn–Hilliard phase field model. The main …

This paper develops novel and robust central discontinuous Galerkin (CDG) schemes of
arbitrarily high-order accuracy for special relativistic magnetohydrodynamics (RMHD) with a …

New integral, finite-volume forms of the Saint-Venant equations for one-dimensional (1-D)
open-channel flow are derived. The new equations are in the flux-gradient conservation …

In this paper, we consider a one-dimensional fully nonlinear weakly dispersive Green–
Naghdi model for shallow water waves over variable bottom topographies. Such model …