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Computational Methods in Applied Mathematics

Editor-in-Chief: Carstensen, Carsten

Managing Editor: Matus, Piotr

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IMPACT FACTOR 2017: 0.658

CiteScore 2017: 1.05

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1609-9389
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Volume 10, Issue 3

Issues

A Natural Adaptive Nonconforming FEM Of Quasi-Optimal Complexity

H. Rabus

Abstract

In recent years, the question on the convergence and optimality in the context of adaptive finite element methods has been the subject of intensive studies. However, for nonstandard FEMs such as mixed or nonconforming ones, the lack of Galerkin's orthogonality requires new mathematical arguments. The presented adap- tive algorithm for the Crouzeix-Raviart finite element method and the Poisson model problem is of quasi-optimal complexity. Furthermore it is natural in the sense that collective marking rather than a separate marking is applied or the estimated error and the volume term.

Keywords: AFEM; adaptive finite element method; nonstandard FEM; nonconform FEM; ANCFEM; optimal convergence; Crouzeix-Raviart

About the article

Received: 2010-07-11

Revised: 2010-07-28

Accepted: 2010-08-29

Published in Print:


Citation Information: Computational Methods in Applied Mathematics Comput. Methods Appl. Math., Volume 10, Issue 3, Pages 315–325, ISSN (Online) 1609-9389, ISSN (Print) 1609-4840, DOI: https://doi.org/10.2478/cmam-2010-0018.

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© Institute of Mathematics, NAS of Belarus. This article is distributed under the terms of the Creative Commons Attribution Non-Commercial License, which permits unrestricted non-commercial use, distribution, and reproduction in any medium, provided the original work is properly cited. BY-NC-ND 4.0

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[2]
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SIAM Journal on Numerical Analysis, 2013, Volume 51, Number 3, Page 1715
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[6]
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[7]
R. Altmann and C. Carstensen
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[9]
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Computers & Mathematics with Applications, 2014, Volume 68, Number 12, Page 2167
[11]
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[12]
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Computers & Mathematics with Applications, 2014, Volume 67, Number 6, Page 1195

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