Adaptive reference elements via harmonic extensions and associated inner modes

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Journal Title
Journal ISSN
Volume Title
A1 Alkuperäisartikkeli tieteellisessä aikakauslehdessä
Date
2020-12-01
Major/Subject
Mcode
Degree programme
Language
en
Pages
17
2272-2288
Series
Computers and Mathematics with Applications, Volume 80, issue 11
Abstract
A non-intrusive extension to the standard p-version of the finite element method is proposed. Meshes with hanging nodes are handled by adapting the reference elements so that the resulting discretisation is always conforming. The shape functions on these adaptive reference elements are not polynomials, but either harmonic extensions of the boundary restrictions of the standard shape functions or solutions to a local Poisson problem. The numerical experiments are taken from computational function theory and the efficiency of the proposed extension resulting in exponential convergence in the quantities of interest is demonstrated.
Description
Keywords
Adaptivity, Finite element method, Harmonic extensions, p-version
Other note
Citation
Hakula, H 2020, ' Adaptive reference elements via harmonic extensions and associated inner modes ', Computers and Mathematics with Applications, vol. 80, no. 11, pp. 2272-2288 . https://doi.org/10.1016/j.camwa.2020.07.019