A Survey of hp-Adaptive Strategies for Elliptic Partial Differential Equations

William F. Mitchell () and Marjorie A. McClain
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William F. Mitchell: National Institute of Standards and Technology, Mathematical and Computational Sciences Division
Marjorie A. McClain: National Institute of Standards and Technology, Mathematical and Computational Sciences Division

Chapter Chapter 10 in Recent Advances in Computational and Applied Mathematics, 2011, pp 227-258 from Springer

Abstract: Abstract 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 demonstrate the exponential convergence rates with two classic test problems.

Keywords: Elliptic partial differential equations; Finite elements; hp-adaptive strategy; hp-FEM; 65N30; 65N50 (search for similar items in EconPapers)
Date: 2011
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-90-481-9981-5_10

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DOI: 10.1007/978-90-481-9981-5_10

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