Journal
APPLIED NUMERICAL MATHEMATICS
Volume 60, Issue 7, Pages 673-688Publisher
ELSEVIER
DOI: 10.1016/j.apnum.2010.03.010
Keywords
Adaptive methods; Nonconforming finite elements; A posteriori error estimation; Convergence rate; Optimal computational complexity
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In this paper, we analyze the convergence and optimal complexity of the usual simple adaptive nonconforming finite element method by using Dorfler collective marking strategy. Based on several basic ingredients, such as the estimator reduction, quasi-orthogonality, local upper bound and so on, we eventually show the convergence of the adaptive algorithm by establishing the reduction of some total error and the quasi-optimal convergence rate. Our analysis does not need the relation between the nonconforming P-1 element and the mixed Raviart-Thomas element. The results of numerical experiments confirm that our adaptive algorithm is optimal. (C) 2010 IMACS. Published by Elsevier B.V. All rights reserved.
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