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Sibirskii Zhurnal Vychislitel'noi Matematiki, 2021, Volume 24, Number 4, Pages 345–363
DOI: https://doi.org/10.15372/SJNM20210402
(Mi sjvm785)
 

A priori error analysis of a stabilized finite-element scheme for an elliptic equation with time-dependent boundary conditions

N. Abou Jmeih, T. El Arwadi, S. Dib

Department of Mathematics, Faculty of Science, Beirut Arab University, Beirut, Lebanon
References:
Abstract: This study aims to implement a numerical scheme in order to find the eigenvalues of the Dirichlet-to-Neumann semigroup. This can be used to check its positivity for non-circular domains. This generalized scheme is analyzed after studying the case of the unit ball, in which an explicit representation for the semigroup was obtained by Peter Lax. After analyzing the generalized scheme, we checked its convergence through numerical simulations that were performed using FreeFem++ software.
Key words: finite element scheme, a priori error analysis, dynamical boundary conditions, Dirichlet-to-Neumann semigroup.
Received: 17.07.2019
Revised: 17.02.2021
Accepted: 14.07.2021
English version:
Numerical Analysis and Applications, 2021, Volume 14, Issue 4, Pages 297–315
DOI: https://doi.org/10.1134/S1995423921040017
Bibliographic databases:
Document Type: Article
MSC: 65M60, 65M12, 65M15
Language: Russian
Citation: N. Abou Jmeih, T. El Arwadi, S. Dib, “A priori error analysis of a stabilized finite-element scheme for an elliptic equation with time-dependent boundary conditions”, Sib. Zh. Vychisl. Mat., 24:4 (2021), 345–363; Num. Anal. Appl., 14:4 (2021), 297–315
Citation in format AMSBIB
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\paper A priori error analysis of a stabilized finite-element scheme for an elliptic equation with time-dependent boundary conditions
\jour Sib. Zh. Vychisl. Mat.
\yr 2021
\vol 24
\issue 4
\pages 345--363
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\crossref{https://doi.org/10.15372/SJNM20210402}
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\jour Num. Anal. Appl.
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\issue 4
\pages 297--315
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