Quasi-Optimality of an AFEM for General Second Order Elliptic PDE

Pal, A and Gudi, T (2024) Quasi-Optimality of an AFEM for General Second Order Elliptic PDE. In: Computational Methods in Applied Mathematics .

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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 b � 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), no. 5, 2524-2550. The theoretical results are illustrated by numerical experiments. © 2024 De Gruyter. All rights reserved.

Item Type:	Journal Article
Publication:	Computational Methods in Applied Mathematics
Publisher:	Walter de Gruyter GmbH
Additional Information:	The copyright for this article belongs to Walter de Gruyter GmbH .
Keywords:	A posteriori estimate; Adaptive finite element; Adaptive finite element methods; Dual problem; Elliptic PDEs; Finite element; Non-self adjoint PDE; Non-self-adjoint; Posteriori estimates; Quasi-optimality, Finite element method
Department/Centre:	Division of Physical & Mathematical Sciences > Mathematics
Date Deposited:	01 Mar 2024 09:30
Last Modified:	01 Mar 2024 09:30
URI:	https://eprints.iisc.ac.in/id/eprint/83990

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