| 二维Poisson方程的Legendre Tau方法的误差估计 |
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| 引用本文： | 沈婷婷,马和平. 二维Poisson方程的Legendre Tau方法的误差估计[J]. 上海大学学报(自然科学版), 2011, 17(3): 275-279. DOI: 10.3969/j.issn.1007-2861.2011.03.012 |
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| 作者姓名： | 沈婷婷 马和平 |
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| 作者单位： | 上海大学理学院,上海,200444 |
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| 基金项目： | 国家自然科学基金资助项目(60874039); 上海市教委重点学科建设资助项目(J50101); 上海大学研究生创新基金资助项目(SHUCX080129) |
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| 摘 要： | 主要考虑用Legendre tau方法求解二维Poisson方程的Dirichlet问题.通过选取带有广义Jacobi权的函数作为检验函数,得到Legendre tau方法对于二维Poisson方程Dirichlet问题的H1模的最优误差估计;然后,通过对偶技巧,得到L2模的最优误差估计;最后,通过数值算例,进一步比较说明理论分析的结果.
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| 关 键 词： | Legendretau方法 二维Poisson方程 最优误差估计 |
Error Estimate of Legendre Tau Method for Two-Dimensional Poisson Equation |
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| SHEN Ting-ting,MA He-ping. Error Estimate of Legendre Tau Method for Two-Dimensional Poisson Equation[J]. Journal of Shanghai University(Natural Science), 2011, 17(3): 275-279. DOI: 10.3969/j.issn.1007-2861.2011.03.012 |
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| Authors: | SHEN Ting-ting MA He-ping |
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| Affiliation: | SHEN Ting-ting,MA He-ping(College of Sciences,Shanghai University,Shanghai 200444,China) |
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| Abstract: | The two-dimensional Poisson equation with homogeneous Dirichlet boundary condition by the Legendre tau method is considered.The optimal rate of convergence in H1-norm of Legendre tau method for the two-dimensional Poisson equation with homogeneous Dirichlet boundary condition is obtained by taking test functions with the generalized Jacobi weight.The optimal convergent rate in L2-norm is proved by the duality argument.Numerical examples are given to verify the analysis results. |
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| Keywords: | Legendre tau method two-dimensional Poisson equation optimal error estimate |
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