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Adaptive $hp$-FEM with Arbitrary-Level Hanging Nodes for Maxwell's Equations

Adaptive $hp$-FEM with Arbitrary-Level Hanging Nodes for Maxwell's Equations
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Year:    2010

Author:    Pavel Solin, Lenka Dubcova, Ivo Dolezel

Advances in Applied Mathematics and Mechanics, Vol. 2 (2010), Iss. 4 : pp. 518–532

Abstract

Adaptive higher-order finite element methods ($hp$-FEM) are well known for their potential of exceptionally fast (exponential) convergence. However, most $hp$-FEM codes remain in an academic setting due to an extreme algorithmic complexity of $hp$-adaptivity algorithms. This paper aims at simplifying $hp$-adaptivity for $H$(curl)-conforming approximations by presenting a novel technique of arbitrary-level hanging nodes. The technique is described and it is demonstrated numerically that it makes adaptive $hp$-FEM more efficient compared to $hp$-FEM on regular meshes and meshes with one-level hanging nodes.

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Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/10.4208/aamm.10-m1012

Advances in Applied Mathematics and Mechanics, Vol. 2 (2010), Iss. 4 : pp. 518–532

Published online:    2010-01

AMS Subject Headings:    Global Science Press

Copyright:    COPYRIGHT: © Global Science Press

Pages:    15

Keywords:   

Author Details

Pavel Solin

Lenka Dubcova

Ivo Dolezel

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