A Comparison of hp-adaptive Strategies for Elliptic Partial Differential Equations

Published

March 5, 2014

Author(s)

William F. Mitchell, Marjorie A. McClain

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

Citation

Mitchell, W. and McClain, M. (2014), A Comparison of hp-adaptive Strategies for Elliptic Partial Differential Equations, ACM Transactions on Mathematical Software (Accessed June 7, 2023)