Mur-Nrdrlec finite element schemes for Maxwell's equations

Global superconvergence for Maxwell's equations

In this paper, the global superconvergence is analysed on two schemes (a mixed finite element scheme and a finite element scheme) for Maxwell’s equations in R3. Such a supercovergence analysis is achieved by means of the technique of integral identity (which has been used in the supercovergence analysis for many other equations and schemes) on a rectangular mesh, and then are generalized into m...

Hodge decomposition for divergence-free vector fields and two-dimensional Maxwell's equations

We propose a new numerical approach for two-dimensional Maxwell's equations that is based on the Hodge decomposition for divergence-free vector fields. In this approach an approximate solution for Maxwell's equations can be obtained by solving standard second order scalar elliptic boundary value problems. This new approach is illustrated by a P 1 finite element method.

Developing Finite Element Methods for Maxwell's Equations in a Cole-Cole Dispersive Medium

In this paper, we consider the time-dependent Maxwell’s equations when Cole–Cole dispersive medium is involved. The Cole–Cole model contains a fractional time derivative term, which couples with the standard Maxwell’s equations in free space and creates some challenges in developing and analyzing time-domain finite element methods for solving this model as mentioned in our earlier work [J. Li, ...

Finite element methods for Maxwell's equations

Edge Element Methods for Maxwell's Equations with Strong Convergence for Gauss' Laws

In this paper we propose and investigate some edge element approximations for three Maxwell systems in three dimensions: the stationary Maxwell equations, the time-harmonic Maxwell equations and the time-dependent Maxwell equations. These approximations have three novel features. First, the resulting discrete edge element systems can be solved by some existing preconditioned solvers with optima...