A Comparison of hp-adaptive Strategies for Elliptic Partial Differential Equations

U.S. Department Of Commerce

ISBN 10: 149531653X / ISBN 13: 9781495316531

Verlag: CreateSpace Independent Publishing Platform, 2014

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Bibliografische Details

• Titel: A Comparison of hp-adaptive Strategies for Elliptic Partial Differential Equations
• Verlag: CreateSpace Independent Publishing Platform
• Erscheinungsjahr: 2014
• Sprache: Englisch
• ISBN-10: 149531653X
• ISBN-13: 9781495316531
• Einband: Softcover
• Zustand: New

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Inhaltsangabe

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.