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.

引用

页码：398 / 417

页数：20

共 37 条

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2-B

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