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An a-posteriori error estimate for \(hp\)-adaptive DG methods for elliptic eigenvalue problems on anisotropically refined meshes

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Abstract

We prove an a-posteriori error estimate for an \(hp\)-adaptive discontinuous Galerkin method for the numerical solution of elliptic eigenvalue problems with discontinuous coefficients on anisotropically refined rectangular elements. The estimate yields a global upper bound of the errors for both the eigenvalue and the eigenfunction and lower bound of the error for the eigenfunction only. The anisotropy of the underlying meshes is incorporated in the upper bound through an alignment measure. We present a series of numerical experiments to test the flexibility and robustness of this approach within a fully automated \(hp\)-adaptive refinement algorithm.

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  1. School of Mathematical Sciences, University of Nottingham, University Park, Nottingham, NG7 2RD, UK

    Stefano Giani & Edward Hall

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  1. Stefano Giani
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  2. Edward Hall
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Correspondence to Edward Hall.

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Giani, S., Hall, E. An a-posteriori error estimate for \(hp\)-adaptive DG methods for elliptic eigenvalue problems on anisotropically refined meshes. Computing 95 (Suppl 1), 319–341 (2013). https://doi.org/10.1007/s00607-012-0261-5

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  • DOI: https://doi.org/10.1007/s00607-012-0261-5

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