A Comparison of hp-adaptive Strategies for Elliptic Partial Differential Equations (long version)

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ISBN 10: 1493745166 / ISBN 13: 9781493745166

Editore: CreateSpace Independent Publishing Platform, 2013

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• Titolo: A Comparison of hp-adaptive Strategies for Elliptic Partial Differential Equations (long version)
• Editore: CreateSpace Independent Publishing Platform
• Data di pubblicazione: 2013
• Lingua: Inglese
• ISBN 10: 1493745166
• ISBN 13: 9781493745166
• Rilegatura: Brossura
• Condizione: New

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Riassunto

The hp version of the finite element method (hp-FEM) combined with adaptive mesh refinement is a particularly efficient method for solving partial differential equations because it can achieve a convergence rate that is exponential in the number of degrees of freedom. hp-FEM allows for refinement in both the element size, h, and the polynomial degree, p. Like adaptive refinement for the h version of the finite element method, a posteriori error estimates can be used to determine where the mesh needs to be refined, but a single error estimate can not simultaneously determine whether it is better to do the refinement by h or by p. Several strategies for making this determination have been proposed over the years. In this paper we summarize these strategies and present the results of a numerical experiment to study the convergence properties of these strategies.