| ADFE METHOD WITH HIGH ACCURACY FOR NONLINEAR PARABOLIC INTEGRO-DIFFERENTIAL SYSTEM WITH NONLINEAR BOUNDARY CONDITIONS |
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| 作者姓名： | 崔霞 |
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| 作者单位： | Cui XiaLaboratory of Computational Physics，Institute of Applied Physics and Computational Mathematics，P.O. Box 8009-26，Beijing 100088，China |
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| 基金项目： | China National Key Program for Developing Basic Sciences（G199903280），Mathematical Tianyuan Foundation and NNSF of China（19932010） |
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| 摘 要： | Alternating direction finite element (ADFE) scheme for d-dimensional nonlin-ear system of parabolic integro-differential equations is studied. By using a local approxi-mation based on patches of finite elements to treat the capacity term qi(u), decomposition of the coefficient matrix is realized; by using alternating direction, the multi-dimensional problem is reduced to a family of single space variable problems, calculation work is sim-plified; by using finite element method, high accuracy for space variant is kept; by using inductive hypothesis reasoning, the difficulty coming from the nonlinearity of the coeffi-cients and boundary conditions is treated; by introducing Ritz-Volterra projection, the difficulty coming from the memory term is solved. Finally, by using various techniques for priori estimate for differential equations, the unique resolvability and convergence proper-ties for both FE and ADFE schemes are rigorously demonstrated, and optimal H1 and L2 norm space estimates and O((△t)2) estim
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ADFE METHOD WITH HIGH ACCURACY FOR NONLINEAR PARABOLIC INTEGRO-DIFFERENTIAL SYSTEM WITH NONLINEAR BOUNDARY CONDITIONS |
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| Cui XiaLaboratory of Computational Physics.ADFE METHOD WITH HIGH ACCURACY FOR NONLINEAR PARABOLIC INTEGRO-DIFFERENTIAL SYSTEM WITH NONLINEAR BOUNDARY CONDITIONS[J].Acta Mathematica Scientia,2002,22(4). |
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| Authors: | Cui XiaLaboratory of Computational Physics |
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| Institution: | Cui XiaLaboratory of Computational Physics,Institute of Applied Physics and Computational Mathematics,P.O. Box 8009-26,Beijing 100088,China |
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| Abstract: | Alternating direction finite element (ADFE) scheme for d-dimensional nonlinear system of parabolic integro-differential equations is studied. By using a local approximation based on patches of finite elements to treat the capacity term qi(u), decomposition of the coefficient matrix is realized; by using alternating direction, the multi-dimensional problem is reduced to a family of single space variable problems, calculation work is simplified; by using finite element method, high accuracy for space variant is kept; by using inductive hypothesis reasoning, the difficulty coming from the nonlinearity of the coefficients and boundary conditions is treated; by introducing Ritz-Volterra projection, the difficulty coming from the memory term is solved. Finally, by using various techniques for priori estimate for differential equations, the unique resolvability and convergence properties for both FE and ADFE schemes are rigorously demonstrated, and optimal H1 and L2norm space estimates and O((△t)2) estimate for time variant are obtained. |
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| Keywords: | Parabolic integro-differential system nonlinear alternating direction finite element high accuracy |
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