数学物理学报 ›› 2014, Vol. 34 ›› Issue (3): 716-726.

• 论文 • 上一篇    下一篇

奇异摄动问题最优阶一致收敛的间断有限元分析

杨宇博|祝鹏|尹云辉   

  1. 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
  • 收稿日期:2012-12-16 修回日期:2013-11-22 出版日期:2014-06-25 发布日期:2014-06-25
  • 基金资助:

    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

A Optimal Uniformly Convergent Discontinuous Galerkin Finite Element Method for Singularly Perturbed Problem

 YANG Yu-Bo, ZHU Peng, YIN Yun-Hui   

  1. Nanhu College, Jiaxing University, Zhejiang Jiaxing 314001; School of Mathematics, Physics and Information, |Jiaxing University, Zhejiang Jiaxing 314001
  • Received:2012-12-16 Revised:2013-11-22 Online:2014-06-25 Published:2014-06-25
  • Supported by:

    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

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.

关键词: 奇异摄动问题, 间断Galerkin有限元, Bakhvalov-Shishkin网格, 一致收敛性

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.

Key words: Singularly perturbed problem, Discontinuous Galerkin finite element method, Bakhvalov-Shishkin mesh, Uniform convergence

中图分类号: 

  • 65N30