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

Published

October 5, 2011

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

NIST Interagency/Internal Report (NISTIR) - 7824

Report Number

7824

NIST Pub Series

NIST Interagency/Internal Report (NISTIR)

Pub Type

NIST Pubs

Download Paper

https://doi.org/10.6028/NIST.IR.7824

Keywords

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

Citation

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], https://doi.org/10.6028/NIST.IR.7824 (Accessed October 11, 2025)