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Nodal O(h4)-superconvergence in 3D by averaging piecewise linear, bilinear, and trilinear FE approximations

SYSNO ASEP	0338973
Document Type	J - Journal Article
R&D Document Type	Journal Article
Subsidiary J	Článek ve WOS
Title	Nodal O(h4)-superconvergence in 3D by averaging piecewise linear, bilinear, and trilinear FE approximations
Author(s)	Hannukainen, A. (FI) Korotov, S. (FI) Křížek, Michal (MU-W)_{RID, SAI, ORCID}
Source Title	Journal of Computational Mathematics - ISSN 0254-9409 Roč. 28, č. 1 (2010), s. 1-10
Number of pages	10 s.
Language	eng - English
Country	CN - China
Keywords	higher order error estimates ; tetrahedral and prismatic elements ; superconvergence ; averaging operators
Subject RIV	BA - General Mathematics
R&D Projects	IAA100190803 GA AV ČR - Academy of Sciences of the Czech Republic (AV ČR)
CEZ	AV0Z10190503 - MU-W (2005-2011)
UT WOS	000274262000001
EID SCOPUS	77649318469
DOI	10.4208/jcm.2009.09-m1004
Annotation	We construct and analyse a nodal O(h4)-superconvergent FE scheme for approximating the Poisson equation with homogeneous boundary conditions in three-dimensional domains by means of piecewise trilinear functions. The scheme is based on averaging the equations that arise from FE approximations on uniform cubic, tetrahedral, and prismatic partitions. This approach presents a three-dimensional generalization of a two-dimensional averaging of linear and bilinear elements which also exhibits nodal O(h4)-superconvergence (ultraconvergence). The obtained superconvergence result is illustrated by two numerical examples.
Workplace	Mathematical Institute
Contact	Jarmila Štruncová, struncova@math.cas.cz, library@math.cas.cz, Tel.: 222 090 757
Year of Publishing	2010

Number of the records: 1