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C-0 elements for generalized indefinite Maxwell equations

C-0 elements for generalized indefinite Maxwell equations

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Original languageEnglish
Pages (from-to)61-99
Number of pages39
JournalNumerische Mathematik
Issue number1
StatePublished - Sep 2012


In this paper we develop the C (0) finite element method for a generalized curlcurl-grad div indefinite Maxwell problem in a Lipschitz domain such as nonconvex polygon for which the solution of the problem may be nonsmooth and only have the H (r) regularity for some r < 1. The ingredients of our method are that two 'mass-lumping' L (2) projectors are applied to curl and div operators in the problem and that C (0) linear element or isoparametric bilinear element enriched with one element-bubble on every triangle element or with two-element-bubbles on every quadrilateral element, respectively, is employed for each component of the nonsmooth solution. Due to the fact that the element-bubbles can be statically eliminated at element levels, our method is essentially three-nodes or four-nodes C (0) Lagrange element method. With two Fortin-type interpolations established, a very technical duality argument is elaborated to estimate the error for the indefinite problem. For the nonsmooth solution having the H (r) regularity where r may vary in the interval [0, 1), we obtain the error bound in an energy norm. Some numerical experiments are performed to confirm the theoretical error bounds.



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