Superconvergence analysis of Yee scheme for metamaterial Maxwell’s equations on non-uniform rectangular meshes

Document Type

Article

Publication Date

1-1-2016

Publication Title

Numerische Mathematik

Volume

134

Issue

4

First page number:

741

Last page number:

781

Abstract

Since the development of Yee scheme back in 1966, it has become one of the most popular simulation tools for modeling electromagnetic wave propagation in various situations. However, its rigorous error analysis on nonuniform rectangular type grids was carried out until 1994 by Monk and Süli. They showed that the Yee scheme is still second-order convergent on a nonuniform mesh even though the local truncation error is only of first order. In this paper, we extend their results to Maxwell’s equations in metamaterials by a simpler proof, and show the second-order superconvergence in space for the true Yee scheme instead of the only semi-discrete form discussed in Monk and Süli’s original work. Numerical results supporting our analysis are presented. © 2015, Springer-Verlag Berlin Heidelberg.

Keywords

35L15; 65N30; 78-08

Language

English

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