| 带弱奇异核非线性积分微分方程的有限元分析 |
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| 引用本文： | 樊明智,王芬玲,牛裕琪,石东洋. 带弱奇异核非线性积分微分方程的有限元分析[J]. 数学的实践与认识, 2012, 42(12): 141-149 |
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| 作者姓名： | 樊明智 王芬玲 牛裕琪 石东洋 |
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| 作者单位： | 1. 许昌学院数学与统计学院,河南许昌,461000
2. 郑州大学数学系,河南郑州,450052 |
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| 基金项目： | 国家自然科学基金，高等学校博士学科点专项科研基金，河南省教育厅自然科学基金 |
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| 摘 要： | 讨论了带弱奇异核的非线性抛物积分微分方程的Hermite型各向异性矩形元逼近.在各向异性网格下导出了关于Riesz投影的L~2和H~1模的误差估计.在半离散和向后欧拉全离散格式下,基于Riesz投影的性质并利用平均值技巧,分别得到了L~2模意义下的最优误差估计.
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| 关 键 词： | 带弱奇异核的非线性抛物积分微分方程 Hermite型各向异性矩形元 最优误差估计 半离散和全离散格式 |
Finite Element Analysis for Nonlinear Integro Differential Equation with Weakly Singular Kernel |
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| FAN Ming-zhi , WANG Fen-ling , Niu Yu-qi , SHI Dong-yang. Finite Element Analysis for Nonlinear Integro Differential Equation with Weakly Singular Kernel[J]. Mathematics in Practice and Theory, 2012, 42(12): 141-149 |
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| Authors: | FAN Ming-zhi WANG Fen-ling Niu Yu-qi SHI Dong-yang |
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| Affiliation: | 1.School of Mathematics and Statistics,Xughang University,Xuchang 461000,China) (2.Deparment of Mathematics,Zhengzhou University,Zhengzhou 450052,China) |
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| Abstract: | An Hermite-type anisotropic rectangular element approximation is discussed for nonlinear parabolic integro-differential equation with a weakly singular kernel.Error estimates in L~2 and H~1 norms of Riesz projection are derived on the anisotropic meshes. Based on the properties of Riesz projection,the optimal order error estimates in L~2 norm are gained by use of mean-value technique under semi-discrete and backward Euler fully-discrete schemes,respectively. |
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| Keywords: | nonlinear parabolic integro-differential equation with weakly singular kernel Hermite-type anisotropic rectangular element the optimal order error estimate semi-discrete and fully-discrete schemes |
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