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Goal-oriented hp-Adaptive Discontinuous Galerkin Finite Element Methods for Elliptic Eigenvalue Problems – 2011, ILAS 2011, Braunschweig 

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A discontinuous Galerkin method, with hp-adaptivity based on the approximate solution of appropriate dual problems, is employed for highly-accurate eigenvalue computations on a collection of benchmark examples with interesting features like discontinuous coefficients and non-convex geometries. The most remarkable advantage of the goal-oriented approach is an effectivity index for eigenvalues very close to one on the all sequence of hp-adaptively refined meshes. The hp-adaptivity algorithm, that we present, automatically adapts locally in either h or p exploiting an estimation of the local smoothness of the computed eigenfunction. This ensures an exponential convergence rate for all considered examples. This contribution is joint work with Luka Grubisic (University of Zagreb, Croatia) and Jeffrey S. Ovall (University of Kentucky, USA).