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|Author(s):||William F. Mitchell; Marjorie A. McClain;|
|Title:||A Survey of hp-Adaptive Strategies for Elliptic Partial Differential Equations|
|Published:||January 03, 2011|
|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.|
|Citation:||Recent Advances in Computational and Applied Mathematics|
|Publisher:||Springer, New York, NY|
|Pages:||pp. 227 - 258|
|Keywords:||elliptic partial differential equations, finite elements, hp-adaptive strategy, hp-FEM|
|PDF version:||Click here to retrieve PDF version of paper (16MB)|