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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
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
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
Linking options:
https://www.mathnet.ru/eng/sjvm785 https://www.mathnet.ru/eng/sjvm/v24/i4/p345
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Abstract page: | 82 | Full-text PDF : | 22 | References: | 24 | First page: | 6 |
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