Mitchell, W.
and McClain, M.
(2014),
A Comparison of hp-adaptive Strategies for Elliptic Partial Differential Equations, ACM Transactions on Mathematical Software
(Accessed June 24, 2025)
Official websites use .gov
A .gov website belongs to an official government organization in the United States.
Secure .gov websites use HTTPS
A lock (
) or https:// means you’ve safely connected to the .gov website. Share sensitive information only on official, secure websites.
A Comparison of hp-adaptive Strategies for Elliptic Partial Differential Equations
Published
Author(s)
,
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
Issues
If you have any questions about this publication or are having problems accessing it, please contact [email protected].
Created March 5, 2014, Updated June 2, 2021