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

A mortar edge element method with nearly optimal convergence for three-dimensional Maxwell's equations

In this paper, we are concerned with mortar edge element methods for solving three-dimensional Maxwell’s equations. A new type of Lagrange multiplier space is introduced to impose the weak continuity of the tangential components of the edge element solutions across the interfaces between neighboring subdomains. The mortar edge element method is shown to have nearly optimal convergence under som...

Convergence and superconvergence of staggered discontinuous Galerkin methods for the three-dimensional Maxwell's equations on Cartesian grids

In this paper, a new type of staggered discontinuous Galerkin methods for the three dimensional Maxwell’s equations is developed and analyzed. The spatial discretization is based on staggered Cartesian grids so that many good properties are obtained. First of all, our method has the advantages that the numerical solution preserves the electromagnetic energy and automatically fulfills a discrete...

Discrete compactness and the approximation of Maxwell's equations in R3

We analyze the use of edge finite element methods to approximate Maxwell’s equations in a bounded cavity. Using the theory of collectively compact operators, we prove h-convergence for the source and eigenvalue problems. This is the first proof of convergence of the eigenvalue problem for general edge elements, and it extends and unifies the theory for both problems. The convergence results are...

A Simple Proof of Convergence for an Edge Element Discretization of Maxwell's Equations

Chapter 8 Curl-conforming Edge Element Methods 8.1 Maxwell's Equations 8.1.1 Introduction

Electromagnetic phenomena can be described by the electric field E, the electric induction D, the current density J as well as the magnetic field H and the magnetic induction B according to Maxwell's equations given by Faraday's law ∂B ∂t + curl E = 0 in lR 3 , (8.1) where according to the Gauss law div B = 0 in lR 3 , (8.2) and Ampère's law ∂D ∂t − curl H + J = 0 in lR 3 , (8.3) where, again o...