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

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 coefficient...

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Published in:Numerische Mathematik 2021-04, Vol.147 (4), p.903-936
Main Authors: Aylwin, Rubén, Jerez-Hanckes, Carlos
Format: Article
Language:English
Subjects:
Mathematical and Computational Engineering
Mathematical and Computational Physics
Mathematical Methods in Physics
Mathematics
Mathematics and Statistics
Numerical Analysis
Numerical and Computational Physics
Simulation
Theoretical
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description 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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subjects Mathematical and Computational Engineering
Mathematical and Computational Physics
Mathematical Methods in Physics
Mathematics
Mathematics and Statistics
Numerical Analysis
Numerical and Computational Physics
Simulation
Theoretical
title 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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