| AN A.D.I.GALERKIN METHOD FOR NONLINEAR PARABOLIC INTEGRO-DIFFERENTIAL EQUATION USING PATCH APPROXIMATION |
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| 引用本文： | 崔霞.AN A.D.I.GALERKIN METHOD FOR NONLINEAR PARABOLIC INTEGRO-DIFFERENTIAL EQUATION USING PATCH APPROXIMATION[J].高等学校计算数学学报(英文版),1999(2). |
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| 作者姓名： | 崔霞 |
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| 作者单位： | Cui XiaLaboratory of Computational Physics Institiute of Applied physics and Computational Mathematics P. O. Box 8009 - 26，Beijing 10088，PRCt Institute of Mathematics Sciences and System Science，Shandong University，Jinan 250100，PRC. |
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| 摘 要： | An A. D. I. Galerkin scheme for three-dimensional nonlinear parabolic integro-differen-tial equation is studied. By using alternating-direction, the three-dimensional problem is reduced to a family of single space variable problems, the calculation is simplified; by using a local approxima-tion of the coefficients based on patches of finite elements, the coefficient matrix is updated at each time step; by using Ritz-Volterra projection, integration by part and other techniques, the influence coming from the integral term is treated; by using inductive hypothesis reasoning, the difficulty coming from the nonlinearity is treated. For both Galerkin and A. D. I. Galerkin schemes the con-vergence properties are rigorously demonstrated, the optimal H~1-norm and L~2-norm estimates are obtained.
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AN A. D. I. GALERKIN METHOD FOR NONLINEAR PARABOLIC INTEGRO-DIFFERENTIAL EQUATION USING PATCH APPROXIMATION |
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| Cui XiaLaboratory of Computational Physics Institiute of Applied physics and Computational Mathematics P. O. Box - ,Beijing ,PRCt Institute of Mathematics Sciences and System Science,Shandong University,Jinan ,PRC..AN A. D. I. GALERKIN METHOD FOR NONLINEAR PARABOLIC INTEGRO-DIFFERENTIAL EQUATION USING PATCH APPROXIMATION[J].Numerical Mathematics A Journal of Chinese Universities English Series,1999(2). |
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| Authors: | Cui XiaLaboratory of Computational Physics Institiute of Applied physics and Computational Mathematics P O Box - Beijing PRCt Institute of Mathematics Sciences and System Science Shandong University Jinan PRC |
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| Institution: | Cui XiaLaboratory of Computational Physics Institiute of Applied physics and Computational Mathematics P. O. Box 8009 - 26,Beijing 10088,PRCt Institute of Mathematics Sciences and System Science,Shandong University,Jinan 250100,PRC. |
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| Abstract: | An A. D. I. Galerkin scheme for three-dimensional nonlinear parabolic integro-differen-tial equation is studied. By using alternating-direction, the three-dimensional problem is reduced to a family of single space variable problems, the calculation is simplified; by using a local approximation of the coefficients based on patches of finite elements, the coefficient matrix is updated at each time step; by using Ritz-Volterra projection, integration by part and other techniques, the influence coming from the integral term is treated; by using inductive hypothesis reasoning, the difficulty coming from the nonlinearity is treated. For both Galerkin and A. D. I. Galerkin schemes, the convergence properties are rigorously demonstrated, the optimal H1-narm and L~(2)-norm estimates are obtained. |
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| Keywords: | nonlinear parabolic integro-differential equation alternating-direction finite element method error estimate |
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