| 三维非线性抛物型积分-微分方程的A.D.I.Galerkin方法及其分析 |
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| 引用本文： | 崔霞.三维非线性抛物型积分-微分方程的A.D.I.Galerkin方法及其分析[J].系统科学与数学,2001,21(3):362-372. |
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| 作者姓名： | 崔霞 |
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| 作者单位： | 北京应用物理与计算数学研究所计算物理实验室 |
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| 基金项目： | 国家教委博士点基金资助课题. |
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| 摘 要： | 研究三维非线性抛物型积分-微分方程的A.D.I.Galerkin方法.通过交替方向,化三维为一维,简化计算;通过Galerkin法,保持高精度.成功处理了Volterra项的影响;对所提Galerkin及A.D.I.Galerkin格式给出稳定性和收敛性分析,得到最佳H1和L2模估计.
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| 关 键 词： | 抛物型积分-微分方程 交替方向 有限元 误差估计. |
| 修稿时间： | 1997年7月21日 |
THE A.D.I. GALERKIN METHODS AND THE ANALYSIS FOR 3-DIMENSIONAL NONLINEAR PARABOLIC INTEGRO-DIFFERENTIAL EQUATION |
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| Xia CUI.THE A.D.I. GALERKIN METHODS AND THE ANALYSIS FOR 3-DIMENSIONAL NONLINEAR PARABOLIC INTEGRO-DIFFERENTIAL EQUATION[J].Journal of Systems Science and Mathematical Sciences,2001,21(3):362-372. |
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| Authors: | Xia CUI |
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| Institution: | Laboratory of Computational Physics, Institute of Applied Physics and Computational Mathematics, Beijing 100088,P.R.China;Institute of Mathematical Sciences and System Science, Shandong University, Jinan 250100,P.R.China |
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| Abstract: | The A. D. I. Galerkin schemes for 3-dimensional nonlinear parabolic integro- differential equation are studied. By using alternating direction, the 3-dimensional problem is reduced to a family of single space Variable problems, the calculating work is simplified; by using Galerkin method, the high accuracy property is obtained. The influence coming from the Volterra term is treated successfully; the stability and convergence properties for both Galerkin and A.D.I. Galerkin schemes are demonstrated, the optical H1-norm and L2-norm estimates are obtained. |
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| Keywords: | Parabolic integro-differential equation alternating direction finite element error estimate |
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