Asymptotic Expansions and Richardson Extrapolation of Approximate Solutions for Second Order Elliptic Problems on Rectangular Domains by Mixed Finite Element Methods

Authors:
Graeme Fairweather;Qun Lin;Yanping Lin;Junping Wang;Shuhua Zhang
Affiliations:
-;-;-;-;-
Venue:
SIAM Journal on Numerical Analysis
Year:
2006

Citing 0
Cited 5

A splitting extrapolation for solving nonlinear elliptic equations with d-quadratic finite elements

Journal of Computational Physics
Asymptotic error expansion and Richardson extrapolation of eigenvalue approximations for second order elliptic problems by the mixed finite element method

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Superconvergence and Extrapolation Analysis of a Nonconforming Mixed Finite Element Approximation for Time-Harmonic Maxwell's Equations

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A Finite Element Splitting Extrapolation for Second Order Hyperbolic Equations

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An algorithm using the finite volume element method and its splitting extrapolation

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Abstract

In this paper asymptotic error expansions for mixed finite element approximations of general second order elliptic problems are derived under rectangular meshes, and the Richardson extrapolation is applied to improve the accuracy of the approximations by two different schemes with the help of an interpolation postprocessing technique. The results of this paper provide new asymptotic expansions and new approximate solutions which are one-order and a half-order higher in accuracy than those obtained in [J. Wang, Math Comp., 56 (1991), pp. 477-503] and [H. Chen, R. E. Ewing, and R. Lazarov, Asymptotic Error Expansion for the Lowest Order Raviart--Thomas Rectangular Mixed Finite Elements, Technical report ISC-97-01, 1997], respectively. As a by-product, we illustrate that all the approximations of higher accuracy can be used to form a class of a posteriori error estimators for the mixed finite element method.