A Comparison of HP-Adaptive Strategies for Elliptic Partial Differential Equations NIST

ISBN: 9781493745166

Published: November 11th 2013

Paperback

220 pages


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A Comparison of HP-Adaptive Strategies for Elliptic Partial Differential Equations  by  NIST

A Comparison of HP-Adaptive Strategies for Elliptic Partial Differential Equations by NIST
November 11th 2013 | Paperback | PDF, EPUB, FB2, DjVu, talking book, mp3, ZIP | 220 pages | ISBN: 9781493745166 | 6.17 Mb

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 ofMoreThe 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.



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