Residual-based a posteriori error estimation for the Maxwell's eigenvalue problem

Daniele Boffi, Lucia Gastaldi, Rodolfo Rodríguez, Ivana Šebestová

Research output: Contribution to journalArticlepeer-review

4 Scopus citations

Abstract

We present an a posteriori estimator of the error in the L2-norm for the numerical approximation of the Maxwell's eigenvalue problem by means of Nédélec finite elements. Our analysis is based on a Helmholtz decomposition of the error and on a superconvergence result between the L2-orthogonal projection of the exact eigenfunction onto the curl of the Nédélec finite element space and the eigenfunction approximation. Reliability of the a posteriori error estimator is proved up to higher order terms, and local efficiency of the error indicators is shown by using a standard bubble functions technique. The behavior of the a posteriori error estimator is illustrated on a numerical test.
Original languageEnglish (US)
Pages (from-to)1710-1732
Number of pages23
JournalIMA Journal of Numerical Analysis
Volume37
Issue number4
DOIs
StatePublished - Oct 1 2017
Externally publishedYes

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