A Comparison of hp-adaptive Strategies for Elliptic Partial Differential Equations (long version)
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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.
Format:Paperback
Language:English
ISBN:1493745166
ISBN13:9781493745166
Release Date:November 2013
Publisher:Createspace Independent Publishing Platform
Length:220 Pages
Weight:1.15 lbs.
Dimensions:0.5" x 8.5" x 11.0"
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