Dr Stefano Giani stefano.giani@durham.ac.uk
Associate Professor
An a-posteriori error estimate for hp-adaptive DG methods for elliptic eigenvalue problems on anisotropically refined meshes
Giani, S.; Hall, E.
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 | Mar 28, 2024 |
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. |
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Copyright Statement
The final publication is available at Springer via http://dx.doi.org/10.1007/s00607-012-0261-5
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