Pal, Arnab ; Gudi, Thirupathi (2024) Quasi-Optimality of an AFEM for General Second Order Elliptic PDE Computational Methods in Applied Mathematics, 25 (1). pp. 173-188. ISSN 1609-4840
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Official URL: https://doi.org/10.1515/cmam-2023-0238
Related URL: http://dx.doi.org/10.1515/cmam-2023-0238
Abstract
In this article, convergence and quasi-optimal rate of convergence of an adaptive finite element method (in short, AFEM) is shown for a general second-order non-selfadjoint elliptic PDE with convection term bE[L∞(Ω)] d and using minimal regularity of the dual problem, i.e., the solution of the dual problem has only H1 -regularity, which extends the result [J. M. Cascon, C. Kreuzer, R. H. Nochetto and K. G. Siebert, Quasi-optimal convergence rate for an adaptive finite element method, SIAM J. Numer. Anal. 46 2008, 5, 2524–2550]. The theoretical results are illustrated by numerical experiments.
| Item Type: | Article |
|---|---|
| Source: | Copyright of this article belongs to Walter de Gruyter GmbH. |
| Keywords: | Finite Element; Adaptive Finite Element; A Posteriori Estimates; Quasi-Optimality,Non-Self Adjoint PDE |
| ID Code: | 141604 |
| Deposited On: | 02 Dec 2025 07:38 |
| Last Modified: | 02 Dec 2025 07:38 |
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