The Defect Iteration of the Finite Element for Elliptic Boundary Value Problems and Petrov-Galerkin Approximation
Year: 1998
Author: Junbin Gao, Yidu Yang, T. M. Shih
Journal of Computational Mathematics, Vol. 16 (1998), Iss. 2 : pp. 152–164
Abstract
In this paper we introduce a Petrov-Galerkin approximation model to the solution of linear and semi-linear elliptic boundary value problems in which piecewise quadratic polynomial space and piecewise linear polynomial space are used as the shape function space and the test function space, respectively. We prove that the approximation order of the standard quadratic finite element can be attained in this Petrov-Galerkin model. Based on the so-called "contractivity" of the interpolation operator, we further prove that the defect iterative sequence of the linear finite element solution converge to the proposed Petrov-Galerkin approximate solution.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/1998-JCM-9149
Journal of Computational Mathematics, Vol. 16 (1998), Iss. 2 : pp. 152–164
Published online: 1998-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 13
Keywords: Petrov-Galerkin approximation defect iteration correction interpolation operator.