AN A POSTERIORI ERROR ESTIMATOR FOR hp-ADAPTIVE DISCONTINUOUS GALERKIN METHODS FOR ELLIPTIC EIGENVALUE PROBLEMS
2012 ◽
Vol 22
(10)
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pp. 1250030
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Keyword(s):
In this paper we present a residual-based a posteriori error estimator for hp-adaptive discontinuous Galerkin methods for elliptic eigenvalue problems. In particular, we use as a model problem the Laplace eigenvalue problem on bounded domains in ℝd, d = 2, 3, with homogeneous Dirichlet boundary conditions. Analogous error estimators can be easily obtained for more complicated elliptic eigenvalue problems. We prove the reliability and efficiency of the residual-based error estimator also for non-convex domains and use numerical experiments to show that, under an hp-adaptation strategy driven by the error estimator, exponential convergence can be achieved, even for non-smooth eigenfunctions.
2009 ◽
Vol 59
(9)
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pp. 2236-2255
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2010 ◽
Vol 234
(10)
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pp. 2903-2915
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2012 ◽
Vol 236
(18)
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pp. 4810-4826
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2013 ◽
Vol 56
(5)
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pp. 887-900
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2012 ◽
Vol 33
(1)
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pp. 212-241
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1996 ◽
Vol 59
(5)
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pp. 949-963
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