Finite Element Methods with Matching and Nonmatching Meshes for Maxwell Equations with Discontinuous Coefficients
Authors:
- Zhiming ChenZCZhiming Chen
- Qiang DuQDQiang Du
- Jun ZouJZJun Zou
- 1 January 2000
- journal article
- Published by Society for Industrial & Applied Mathematics (SIAM) in SIAM Journal on Numerical Analysis
- Vol. 37 (5) , 1542-1570
Abstract
We investigate the finite element methods for solving time-dependent Maxwell equations with discontinuous coefficients in general three-dimensional Lipschitz polyhedral domains. Both matching and nonmatching finite element meshes on the interfaces are considered, and optimal error estimates for both cases are obtained. The analysis of the latter case is based on an abstract framework for nested saddle point problems, along with a characterization of the trace space for H(curl;D), a new extension theorem for H(curl;D) functions in any Lipschitz domain D, and a novel compactness argument for deriving discrete inf-sup conditions.Keywords
This publication has 26 references indexed in Scilit:
- Fully discrete finite element approaches for time-dependent Maxwell's equationsNumerische Mathematik, 1999
- Vector potentials in three-dimensional non-smooth domainsMathematical Methods in the Applied Sciences, 1998
- Finite element methods and their convergence for elliptic and parabolic interface problemsNumerische Mathematik, 1998
- Least-Squares Finite Element Approximations to Solutions of Interface ProblemsSIAM Journal on Numerical Analysis, 1998
- Finite element convergence for the Darwin model to Maxwell's equationsESAIM: Mathematical Modelling and Numerical Analysis, 1997
- A finite element method for interface problems in domains with smooth boundaries and interfacesAdvances in Computational Mathematics, 1996
- Mathematical Methods in Electromagnetism1996
- A finite element formulation of the Darwin PIC model for use on unstructured gridsJournal of Computational Physics, 1995
- On a Finite-Element Method for Solving the Three-Dimensional Maxwell EquationsJournal of Computational Physics, 1993
- An analysis of the Darwin model of approximation to Maxwell’s equationsForum Mathematicum, 1992