Imposing orthogonality to hierarchic higher-order finite elements

0335929 - MÚ 2010 RIV NL eng J - Journal Article
Šolín, P. - Vejchodský, Tomáš - Zítka, M. - Ávila, F.
Imposing orthogonality to hierarchic higher-order finite elements.
Mathematics and Computers in Simulation. Roč. 76, 1-3 (2007), s. 211-217. ISSN 0378-4754. E-ISSN 1872-7166
R&D Projects: GA ČR GP201/04/P021
Institutional research plan: CEZ:AV0Z10190503
Keywords : optimal shape functions * energetic inner product * Laplace equation * symmetric linear elliptic problems * numerical experiments * hp-finite element method
Subject RIV: BA - General Mathematics
Impact factor: 0.738, year: 2007

We propose a new class of hierarchic higher-order finite elements suitable for the hp-finite element method discretization of symmetric linear elliptic problems. These elements use shape functions which are partially orthonormal on the reference domain under the energetic inner product induced by the elliptic problem. We present numerical experiments showing excellent conditioning properties of the new partially orthogonal shape functions compared to other popular sets of hierarchic shape functions.
Permanent Link: http://hdl.handle.net/11104/0180272