Giani, S. and 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.
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.
|Keywords:||Discontinuous Galerkin methods, Elliptic eigenvalue problems, A posteriori error estimation, hp-adaptivity, Anisotropic mesh refinement.|
|Full text:||(AM) Accepted Manuscript|
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|Publisher Web site:||http://dx.doi.org/10.1007/s00607-012-0261-5|
|Publisher statement:||The final publication is available at Springer via http://dx.doi.org/10.1007/s00607-012-0261-5|
|Date accepted:||05 December 2012|
|Date deposited:||13 October 2015|
|Date of first online publication:||May 2013|
|Date first made open access:||No date available|
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