Error Reduction, Convergence and Optimality for Adaptive Mixed Finite Element Methods for Diffusion Equations
Year: 2012
Journal of Computational Mathematics, Vol. 30 (2012), Iss. 5 : pp. 483–503
Abstract
Error reduction, convergence and optimality are analyzed for adaptive mixed finite element methods (AMFEM) for diffusion equations without marking the oscillation of data. Firstly, the quasi-error, i.e. the sum of the stress variable error and the scaled error estimator, is shown to reduce with a fixed factor between two successive adaptive loops, up to an oscillation. Secondly, the convergence of AMFEM is obtained with respect to the quasi-error plus the divergence of the flux error. Finally, the quasi-optimal convergence rate is established for the total error, i.e. the stress variable error plus the data oscillation.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/jcm.1112-m3480
Journal of Computational Mathematics, Vol. 30 (2012), Iss. 5 : pp. 483–503
Published online: 2012-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 21
Keywords: Adaptive mixed finite element method Error reduction Convergence Quasi-optimal convergence rate.
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