A simple proof of convergence for an edge element discretization of Maxwell’s equations. (English) Zbl 1031.65122
Carstensen, Carsten (ed.) et al., Computational electromagnetics. Proceedings of the GAMM workshop on computational electromagnetics, Kiel, Germany, January 26-28, 2001. Berlin: Springer. Lect. Notes Comput. Sci. Eng. 28, 127-141 (2003).
Summary: The time harmonic Maxwell’s equations for a lossless medium are neither elliptic or definite. Hence the analysis of numerical schemes for these equations presents some unusual difficulties. In this paper we give a simple proof, based on the use of duality, for the convergence of edge finite element methods applied to the cavity problem for Maxwell’s equations. The cavity is assumed to be a general Lipschitz polyhedron, and the mesh is assumed to be regular but not quasi-uniform.
For the entire collection see [Zbl 1007.78001].
For the entire collection see [Zbl 1007.78001].
MSC:
| 65N12 | Stability and convergence of numerical methods for boundary value problems involving PDEs |
| 65N30 | Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs |
| 78A25 | Electromagnetic theory (general) |
| 35Q60 | PDEs in connection with optics and electromagnetic theory |
| 78M10 | Finite element, Galerkin and related methods applied to problems in optics and electromagnetic theory |
