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

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Author(s): William F. Mitchell; Marjorie A. McClain;
Title: A Comparison of hp-adaptive Strategies for Elliptic Partial Differential Equations
Published: March 05, 2014
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 present the results of a numerical experiment to study the convergence properties of these strategies.
Citation: ACM Transactions on Mathematical Software
Keywords: elliptic partial differential equations; finite elements; hp-adaptive strategy; hp-FEM
Research Areas: Software