A note on the design of \(hp\)-adaptive finite element methods for elliptic partial differential equations
type: Item
instance of: scholarly article
title: A note on the design of \(hp\)-adaptive finite element methods for elliptic partial differential equations
zbMATH Open document ID: 1074.65131
author: Paul Houston
author: Endre Süli
published in: Computer Methods in Applied Mechanics and Engineering
publication date: 2005-05-12T00:00:00Z
review text: The design of an automatic mesh modification strategy that is capable of exploiting both local \(h\)- and \(p\)-refinement is studied. The main focus of the paper is to provide a complete account of the design of a fully automatic \(hp\)-adaptive algorithm for the finite element approximation to a one-dimensional reaction-diffusion equation [cf. \textit{P. K. Moore}, Numer. Math. 94, 367--401 (2003; Zbl 1033.65067)]. Some numerical experiments to highlight the practical performance of the proposed \(hp\)-adaptive finite element algorithm are also given.
reviewed by: H. P. Dikshit
Mathematics Subject Classification ID: 65N30
Mathematics Subject Classification ID: 65N15
Mathematics Subject Classification ID: 35J25
zbMATH DE Number: 2167969
zbMATH Keywords: \(hp\)-finite element methods
zbMATH Keywords: a posteriori error analysis
zbMATH Keywords: adaptivity
zbMATH Keywords: automatic mesh modification
zbMATH Keywords: reaction-diffusion equation
zbMATH Keywords: numerical experiments
zbMATH Keywords: algorithm
MaRDI profile type: Publication
full work available at URL: j.cma.2004.04.009
OpenAlex ID: W2045214757
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DOI: 10.1016/J.CMA.2004.04.009
description: scientific article; zbMATH DE number 2167969