The effect of quadrature rules on finite element solutions of Maxwell variational problems: Consistency estimates on meshes with straight and curved elements

Rubén Aylwin, Carlos Jerez-Hanckes

Research output: Contribution to journalArticlepeer-review

Abstract

We study the effects of numerical quadrature rules on error convergence rates when solving Maxwell-type variational problems via the curl-conforming or edge finite element method. A complete a priori error analysis for the case of bounded polygonal and curved domains with non-homogeneous coefficients is provided. We detail sufficient conditions with respect to mesh refinement and precision for the quadrature rules so as to guarantee convergence rates following that of exact numerical integration. On curved domains, we isolate the error contribution of numerical quadrature rules.

Original languageEnglish
Pages (from-to)903-936
Number of pages34
JournalNumerische Mathematik
Volume147
Issue number4
DOIs
StatePublished - Apr 2021

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