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Higher-order finite elements based on generalized eigenfunctions of the Laplacian
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SYSNO ASEP 0321738 Document Type J - Journal Article R&D Document Type Journal Article Subsidiary J Článek ve WOS Title Higher-order finite elements based on generalized eigenfunctions of the Laplacian Title Metody konečných prvků vyšších řádů založené na zobecněných vlastních funkcích Laplacianu Author(s) Šolín, Pavel (UT-L) RID
Vejchodský, Tomáš (MU-W) RID, SAI, ORCIDSource Title International Journal for Numerical Methods in Engineering. - : Wiley - ISSN 0029-5981
Roč. 73, č. 10 (2008), s. 1374-1394Number of pages 21 s. Language eng - English Country US - United States Keywords hp-FEM ; optimal shape functions ; generalized eigenfunctions Subject RIV JA - Electronics ; Optoelectronics, Electrical Engineering R&D Projects GA102/05/0629 GA ČR - Czech Science Foundation (CSF) GA102/07/0496 GA ČR - Czech Science Foundation (CSF) IAA100760702 GA AV ČR - Academy of Sciences of the Czech Republic (AV ČR) GP201/04/P021 GA ČR - Czech Science Foundation (CSF) CEZ AV0Z10190503 - MU-W (2005-2011) AV0Z20570509 - UE-C, UT-L (2005-2011) UT WOS 000253694300002 DOI 10.1002/nme.2129 Annotation We present a new class of higher-order finite elements based on generalized eigenfunctions of the Laplace operatot, which are suitable for both product and simplicial geometries in R^d. Due to simultaneous orthogonality of the generalized eigenfunctions under both the H^1_0 and L^2 products and their almost negligible dependence on reference maps, such finite elements are an excellent choise for the discretization of second-order elliptic problems by the hp-FEM. Analysis is illustrated by numerical results and comparisons with other popular higher-order finite elements are presented. The new elements are used to compute efficiently the model of an electrostatic micromotor. Workplace Institute of Thermomechanics Contact Marie Kajprová, kajprova@it.cas.cz, Tel.: 266 053 154 ; Jana Lahovská, jaja@it.cas.cz, Tel.: 266 053 823 Year of Publishing 2009
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