Richardson extrapolation and defect correction of mixed finite element methods for integro-differential equations in porous media

Shanghui Jia; Deli Li; Tang Liu; Shu Hua Zhang

Applications of Mathematics (2008)

  • Volume: 53, Issue: 1, page 13-39
  • ISSN: 0862-7940

Abstract

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Asymptotic error expansions in the sense of L ∞ -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.

How to cite

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Jia, Shanghui, et al. "Richardson extrapolation and defect correction of mixed finite element methods for integro-differential equations in porous media." Applications of Mathematics 53.1 (2008): 13-39. <http://eudml.org/doc/33309>.

@article{Jia2008,
abstract = {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.},
author = {Jia, Shanghui, Li, Deli, Liu, Tang, Zhang, Shu Hua},
journal = {Applications of Mathematics},
keywords = {integro-differential equations; mixed finite element methods; mixed regularized Green’s functions; asymptotic expansions; interpolation defect correction; interpolation postprocessing; a posteriori error estimators; integro-differential equations; mixed finite element methods; mixed regularized Green's functions},
language = {eng},
number = {1},
pages = {13-39},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Richardson extrapolation and defect correction of mixed finite element methods for integro-differential equations in porous media},
url = {http://eudml.org/doc/33309},
volume = {53},
year = {2008},
}

TY - JOUR
AU - Jia, Shanghui
AU - Li, Deli
AU - Liu, Tang
AU - Zhang, Shu Hua
TI - Richardson extrapolation and defect correction of mixed finite element methods for integro-differential equations in porous media
JO - Applications of Mathematics
PY - 2008
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 53
IS - 1
SP - 13
EP - 39
AB - 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.
LA - eng
KW - integro-differential equations; mixed finite element methods; mixed regularized Green’s functions; asymptotic expansions; interpolation defect correction; interpolation postprocessing; a posteriori error estimators; integro-differential equations; mixed finite element methods; mixed regularized Green's functions
UR - http://eudml.org/doc/33309
ER -

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