Discontinuous Galerkin Methods for Eigenvalue Problems on Anisotropic Meshes

E. J. C. Hall () and S. Giani ()
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E. J. C. Hall: University of Nottingham, School of Mathematical Sciences
S. Giani: University of Nottingham, School of Mathematical Sciences

A chapter in Numerical Mathematics and Advanced Applications 2011, 2013, pp 351-359 from Springer

Abstract: Abstract We derive a goal-oriented a posteriori error estimate for hp-adaptive discontinuous Galerkin discretizations of convection-diffusion eigenvalue problems. We consider one-irregular meshes consisting of parallelograms. The estimate yields very accurate measurements of the errors in the two target functionals considered in this paper. The accuracy of our error estimator is also confirmed by the effectivity index very close to 1 in all numerical tests. We apply our goal-oriented estimator as an error indicator in an anisotropic hp-adaptive refinement algorithm and illustrate its practical performance in a series of numerical examples.

Keywords: Posteriori Error; Discontinuous Galerkin; Discontinuous Galerkin Method; Dual Solution; Posteriori Error Estimate (search for similar items in EconPapers)
Date: 2013
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-642-33134-3_38

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DOI: 10.1007/978-3-642-33134-3_38

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