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The effect of quadrature rules on finite element solutions of Maxwell variational problems

Consistency estimates on meshes with straight and curved elements

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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.

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Authors and Affiliations

  1. School of Engineering, Pontificia Universidad Católica de Chile, Santiago, Chile

    Rubén Aylwin

  2. Faculty of Engineering and Sciences, Universidad Adolfo Ibáñez, Santiago, Chile

    Carlos Jerez-Hanckes

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  1. Rubén Aylwin
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  2. Carlos Jerez-Hanckes
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Correspondence to Carlos Jerez-Hanckes.

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This work was supported in part by Fondecyt Regular 1171491 and doctoral grant Conicyt-PFCHA 2017-21171791.

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Aylwin, R., Jerez-Hanckes, C. The effect of quadrature rules on finite element solutions of Maxwell variational problems. Numer. Math. 147, 903–936 (2021). https://doi.org/10.1007/s00211-021-01186-8

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