Edge element computation of Maxwell's eigenvalues on general quadrilateral meshes

Daniele Boffi; Fumio Kikuchi; Joachim Schöberl

doi:10.1142/S0218202506001145

Edge element computation of Maxwell's eigenvalues on general quadrilateral meshes

Daniele Boffi, Fumio Kikuchi, Joachim Schöberl

Research output: Contribution to journal › Article › peer-review

26 Scopus citations

Abstract

Recent results prove that Nédélec edge elements do not achieve optimal rate of approximation on general quadrilateral meshes. In particular, lowest order edge elements provide stable but non-convergent approximation of Maxwell's eigenvalues. In this paper we analyze a modification of standard edge element that restores the optimality of the convergence. This modification is based on a projection technique that can be interpreted as a reduced integration procedure. © World Scientific Publishing Company.

Original language	English (US)
Pages (from-to)	265-273
Number of pages	9
Journal	Mathematical Models and Methods in Applied Sciences
Volume	16
Issue number	2
DOIs	https://doi.org/10.1142/S0218202506001145
State	Published - Feb 1 2006
Externally published	Yes

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abstract = "Recent results prove that N{\'e}d{\'e}lec edge elements do not achieve optimal rate of approximation on general quadrilateral meshes. In particular, lowest order edge elements provide stable but non-convergent approximation of Maxwell's eigenvalues. In this paper we analyze a modification of standard edge element that restores the optimality of the convergence. This modification is based on a projection technique that can be interpreted as a reduced integration procedure. {\textcopyright} World Scientific Publishing Company.",

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AU - Boffi, Daniele

AU - Kikuchi, Fumio

AU - Schöberl, Joachim

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PY - 2006/2/1

Y1 - 2006/2/1

N2 - Recent results prove that Nédélec edge elements do not achieve optimal rate of approximation on general quadrilateral meshes. In particular, lowest order edge elements provide stable but non-convergent approximation of Maxwell's eigenvalues. In this paper we analyze a modification of standard edge element that restores the optimality of the convergence. This modification is based on a projection technique that can be interpreted as a reduced integration procedure. © World Scientific Publishing Company.

AB - Recent results prove that Nédélec edge elements do not achieve optimal rate of approximation on general quadrilateral meshes. In particular, lowest order edge elements provide stable but non-convergent approximation of Maxwell's eigenvalues. In this paper we analyze a modification of standard edge element that restores the optimality of the convergence. This modification is based on a projection technique that can be interpreted as a reduced integration procedure. © World Scientific Publishing Company.

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EP - 273

JO - Mathematical Models and Methods in Applied Sciences

JF - Mathematical Models and Methods in Applied Sciences

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ER -

Edge element computation of Maxwell's eigenvalues on general quadrilateral meshes

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