| 奇异摄动问题最优阶一致收敛的间断有限元分析 |
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| 引用本文： | 杨宇博,祝鹏,尹云辉.奇异摄动问题最优阶一致收敛的间断有限元分析[J].数学物理学报(A辑),2014,34(3):716-726. |
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| 作者姓名： | 杨宇博 祝鹏 尹云辉 |
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| 作者单位： | 嘉兴学院 南湖学院 浙江 嘉兴 314001；嘉兴学院 数理与信息工程学院 浙江 嘉兴 314001 |
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| 基金项目： | 浙江省自然科学基金(LQ12A01014)、 浙江省教育厅科研项目(Y201330020)和嘉兴学院科研启动基金(70510017)资助 |
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| 摘 要： | 采用非对称内罚间断有限元方法(以下简称NIPG方法)求解一维对流扩散型奇异摄动问题.理论上证明了采用拉格朗日线性元的NIPG方法在Bakhvalov-Shishkin网格上具有最优阶的一致收敛性,即在能量范数度量下其误差估计为O(N~(-1)),其中N为网格剖分中单元个数.数值算例验证了理论分析的正确性.
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| 关 键 词： | 奇异摄动问题 间断Galerkin有限元 Bakhvalov-Shishkin网格 一致收敛性 |
| 收稿时间： | 2012-12-16 |
| 修稿时间： | 2013-11-22 |
A Optimal Uniformly Convergent Discontinuous Galerkin Finite Element Method for Singularly Perturbed Problem |
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| YANG Yu-Bo,ZHU Peng,YIN Yun-Hui.A Optimal Uniformly Convergent Discontinuous Galerkin Finite Element Method for Singularly Perturbed Problem[J].Acta Mathematica Scientia,2014,34(3):716-726. |
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| Authors: | YANG Yu-Bo ZHU Peng YIN Yun-Hui |
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| Institution: | Nanhu College, Jiaxing University, Zhejiang Jiaxing 314001； School of Mathematics, Physics and Information, |Jiaxing University, Zhejiang Jiaxing 314001 |
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| Abstract: | A nonsymmetric discontinuous Galerkin finite element method with interior penalties is considered for one-dimensional
singularly perturbed convection-diffusion problem. On a Bakhvalov-Shishkin mesh with Lagrange linear elements, the method is shown to be convergent, uniformly in the perturbation parameter ε, of optimal error O(N-1) in the energy
norm, where N is the number of mesh. Finally, through numerical experiments, the authers verified the theoretical result. |
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| Keywords: | Singularly perturbed problemzz Discontinuous Galerkin finite element methodzz Bakhvalov-Shishkin meshzz Uniform convergencezz |
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