Mitchell, W.
and McClain, M.
(2014),
A Comparison of hp-adaptive Strategies for Elliptic Partial Differential Equations, ACM Transactions on Mathematical Software
(Accessed June 1, 2025)
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A Comparison of hp-adaptive Strategies for Elliptic Partial Differential Equations
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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
Pub Type
Journals
Keywords
elliptic partial differential equations, finite elements, hp-adaptive strategy, hp-FEM
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Created March 5, 2014, Updated June 2, 2021