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A Comparison of hp-adaptive Strategies for Elliptic Partial Differential Equations (long version)



William F. Mitchell, Marjorie A. McClain


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.
NIST Interagency/Internal Report (NISTIR) - 7824
Report Number


elliptic partial differential equations, finite elements, hp-adaptive strategy, hp-FEM


Mitchell, W. and McClain, M. (2011), A Comparison of hp-adaptive Strategies for Elliptic Partial Differential Equations (long version), NIST Interagency/Internal Report (NISTIR), National Institute of Standards and Technology, Gaithersburg, MD, [online], (Accessed May 22, 2024)


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Created October 5, 2011, Updated June 2, 2021