| A Comparison of hp-adaptive Strategies for Elliptic Partial Differential Equations Contributor(s): U. S. Department of Commerce (Author) |
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ISBN: 149531653X ISBN-13: 9781495316531 Publisher: Createspace Independent Publishing Platform OUR PRICE: $12.34 Product Type: Paperback Published: January 2014 |
| Additional Information |
| BISAC Categories: - Reference |
| Physical Information: 0.46" H x 8.5" W x 11.02" (1.13 lbs) 216 pages |
| Descriptions, Reviews, Etc. |
| Publisher Description: 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. |