| THE DEFECT ITERATION OF THE FINITE ELEMENT FOR ELLIPTIC BOUNDARY VALUE PROBLEMS AND PETROV-GALERKIN APPROXIMATION |
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| 作者单位： | Jun-bin Gao (Department of Mathematics，Huazhong University of Science and Technology，Wuhan 430074，China)Yi-du Yang(Department of Mathematics，Guizhou Normal University，Guiyang 550001，China)T.M. Shih (Department of Applied Mathematics，The Hong Kong Po |
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| 摘 要： | 1.IntroductionFranketc.of.l]establishedtheiterateddefectcorrectionschemeforfiniteelemelltofellipticboundaryproblems.FOrlinearellipticboundaryvalueproblem2--5]havediscllssedtheefficiencyoftheschemebyusillgsuperconvergenceandasymptoticexpansion"lidertheco…
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THE DEFECT ITERATION OF THE FINITE ELEMENT FOR ELLIPTIC BOUNDARY VALUE PROBLEMS AND PETROV-GALERKIN APPROXIMATION |
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| Authors: | Jun-bin Gao |
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| 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 sohution. |
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| Keywords: | Petrov-Galerkin approximation defect iteration correction interpolation operator |
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