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Title: Richardson extrapolation and defect correction of mixed finite element methods for integro-differential equations in porous media (English)
Author: Jia, Shanghui
Author: Li, Deli
Author: Liu, Tang
Author: Zhang, Shuhua
Language: English
Journal: Applications of Mathematics
ISSN: 0862-7940
Volume: 53
Issue: 1
Year: 2008
Pages: 13-39
Summary lang: English
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Category: math
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Summary: Asymptotic error expansions in the sense of $L^{\infty }$-norm for the Raviart-Thomas mixed finite element approximation by the lowest-order rectangular element associated with a class of parabolic integro-differential equations on a rectangular domain are derived, such that the Richardson extrapolation of two different schemes and an interpolation defect correction can be applied to increase the accuracy of the approximations for both the vector field and the scalar field by the aid of an interpolation postprocessing technique, and the key point in deriving them is the establishment of the error estimates for the mixed regularized Green’s functions with memory terms presented in R. Ewing at al., Int. J. Numer. Anal. Model 2 (2005), 301–328. As a result of all these higher order numerical approximations, they can be used to generate a posteriori error estimators for this mixed finite element approximation. (English)
Keyword: integro-differential equations
Keyword: mixed finite element methods
Keyword: mixed regularized Green’s functions
Keyword: asymptotic expansions
Keyword: interpolation defect correction
Keyword: interpolation postprocessing
Keyword: a posteriori error estimators
MSC: 45K05
MSC: 65M12
MSC: 65M60
MSC: 65R20
MSC: 76M10
MSC: 76S05
idZBL: Zbl 1177.76408
idMR: MR2382288
DOI: 10.1007/s10492-008-0011-3
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Date available: 2009-09-22T18:32:02Z
Last updated: 2015-05-17
Stable URL: http://hdl.handle.net/10338.dmlcz/134697
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