| 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 |
| Research Areas: |
Software |
| PDF version: |
 Click here to retrieve PDF version of paper (15MB) |
