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arXiv · 1602.00675

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

Daniele Boffi·Lucia Gastaldi·Rodolfo Rodríguez·Ivana Šebestová
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Abstract

We present an a posteriori estimator of the error in the L^2-norm for the numerical approximation of the Maxwell's eigenvalue problem by means of N\'ed\'elec finite elements. Our analysis is based on a Helmholtz decomposition of the error and on a superconvergence result between the L^2-orthogonal projection of the exact eigenfunction onto the curl of the N\'ed\'elec 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.

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Daniele Boffi, Lucia Gastaldi, Rodolfo Rodríguez, Ivana Šebestová. 2016-02-01. Residual-based a posteriori error estimation for the Maxwell's eigenvalue problem. https://arxiv.org/abs/1602.00675

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