A NODAL-BASED FINITE ELEMENT APPROXIMATION OF THE MAXWELL PROBLEM SUITABLE FOR SINGULAR SOLUTIONS

被引：38
|
作者：
Badia, Santiago [1 ]
Codina, Ramon [2 ]
机构：
[1] UPC, CIMNE, Castelldefels 08860, Spain
[2] Univ Politecn Cataluna, ES-08034 Barcelona, Spain
来源：
SIAM JOURNAL ON NUMERICAL ANALYSIS | 2012年 / 50卷 / 02期
基金：
欧洲研究理事会;
关键词：
finite elements; Maxwell equations; singular solutions; nodal elements; stabilization techniques; DISCONTINUOUS GALERKIN METHOD; EQUATIONS; FORMULATION; DOMAINS;
D O I：
10.1137/110835360
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
A new mixed finite element approximation of Maxwell's problem is proposed, its main features being that it is based on a novel augmented formulation of the continuous problem and the introduction of a mesh dependent stabilizing term, which yields a very weak control on the divergence of the unknown. The method is shown to be stable and convergent in the natural H(curl 0;Omega) norm for this unknown. In particular, convergence also applies to singular solutions, for which classical nodal-based interpolations are known to suffer from spurious convergence upon mesh refinement.
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页码：398 / 417
页数：20
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