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

Giani, S.; Hall, E.

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


Authors

E. Hall



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.

Citation

Giani, S., & Hall, E. (2013). An a-posteriori error estimate for hp-adaptive DG methods for elliptic eigenvalue problems on anisotropically refined meshes. Computing, 95(1 Supplement), S319-S341. https://doi.org/10.1007/s00607-012-0261-5

Journal Article Type Article
Acceptance Date Dec 5, 2012
Publication Date May 1, 2013
Deposit Date Feb 12, 2013
Publicly Available Date Oct 13, 2015
Journal Computing
Print ISSN 0010-485X
Electronic ISSN 1436-5057
Publisher Springer
Peer Reviewed Peer Reviewed
Volume 95
Issue 1 Supplement
Pages S319-S341
DOI https://doi.org/10.1007/s00607-012-0261-5
Keywords Discontinuous Galerkin methods, Elliptic eigenvalue problems, A posteriori error estimation, hp-adaptivity, Anisotropic mesh refinement.
Public URL https://durham-repository.worktribe.com/output/1497342

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