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A Posteriori Error Estimates for Maxwell’s Eigenvalue Problem

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Abstract

We introduce a residual error indicator for the Nédélec finite element approximation of the eigenmodes of the Maxwell cavity problem. By using the known equivalence with a mixed problem we prove reliability and efficiency of the error indicator. Numerical results confirm the optimal behavior of an adaptive scheme based on the error indicator.

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Acknowledgements

First author gratefully acknowledges the hospitality of University of Concepción (Departamento de Ingeniería Matemática and CI\(^2\)MA) during his visit on January 2016. First and second authors were partially funded by IMATI-CNR and GNCS-INDAM. Third author was partially supported by BASAL project CMM, Universidad de Chile (Chile). Fourth author was supported by Fondecyt Postdoctoral Grant No. 3150047, CONICYT (Chile).

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Authors and Affiliations

  1. Dipartimento di Matematica “F. Casorati”, Università di Pavia, Pavia, Italy

    Daniele Boffi

  2. DICATAM Sez. di Matematica, Università di Brescia, Brescia, Italy

    Lucia Gastaldi

  3. CI2MA, Departamento de Ingeniería Matemática, Universidad de Concepción, Casilla 160-C, Concepción, Chile

    Rodolfo Rodríguez & Ivana Šebestová

Authors
  1. Daniele Boffi
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  2. Lucia Gastaldi
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  3. Rodolfo Rodríguez
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  4. Ivana Šebestová
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Corresponding author

Correspondence to Rodolfo Rodríguez.

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Boffi, D., Gastaldi, L., Rodríguez, R. et al. A Posteriori Error Estimates for Maxwell’s Eigenvalue Problem. J Sci Comput 78, 1250–1271 (2019). https://doi.org/10.1007/s10915-018-0808-5

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  • DOI: https://doi.org/10.1007/s10915-018-0808-5

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