Volume 2, Issue 4
Adaptive hp-FEM with Arbitrary-Level Hanging Nodes for Maxwell's Equations

Pavel Solin, Lenka Dubcova & Ivo Dolezel

Adv. Appl. Math. Mech., 2 (2010), pp. 518-532.

Published online: 2010-02

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  • 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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@Article{AAMM-2-518, author = {Pavel Solin, Lenka Dubcova and Ivo Dolezel}, title = {Adaptive hp-FEM with Arbitrary-Level Hanging Nodes for Maxwell's Equations}, journal = {Advances in Applied Mathematics and Mechanics}, year = {2010}, volume = {2}, number = {4}, pages = {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.

}, issn = {2075-1354}, doi = {https://doi.org/10.4208/aamm.10-m1012}, url = {http://global-sci.org/intro/article_detail/aamm/8344.html} }
TY - JOUR T1 - Adaptive hp-FEM with Arbitrary-Level Hanging Nodes for Maxwell's Equations AU - Pavel Solin, Lenka Dubcova & Ivo Dolezel JO - Advances in Applied Mathematics and Mechanics VL - 4 SP - 518 EP - 532 PY - 2010 DA - 2010/02 SN - 2 DO - http://doi.org/10.4208/aamm.10-m1012 UR - https://global-sci.org/intro/article_detail/aamm/8344.html KW - AB -

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.

Pavel Solin, Lenka Dubcova & Ivo Dolezel. (1970). Adaptive hp-FEM with Arbitrary-Level Hanging Nodes for Maxwell's Equations. Advances in Applied Mathematics and Mechanics. 2 (4). 518-532. doi:10.4208/aamm.10-m1012
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