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

0338973 - MÚ 2010 RIV CN eng J - Journal Article
Hannukainen, A. - Korotov, S. - Křížek, Michal
Nodal O(h4)-superconvergence in 3D by averaging piecewise linear, bilinear, and trilinear FE approximations.
Journal of Computational Mathematics. Roč. 28, č. 1 (2010), s. 1-10. ISSN 0254-9409. E-ISSN 1991-7139
R&D Projects: GA AV ČR(CZ) IAA100190803
Institutional research plan: CEZ:AV0Z10190503
Keywords : higher order error estimates * tetrahedral and prismatic elements * superconvergence * averaging operators
Subject RIV: BA - General Mathematics
Impact factor: 0.760, year: 2010
http://www.jstor.org/stable/43693564

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.
Permanent Link: http://hdl.handle.net/11104/0182614