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奇异摄动问题 FEM/LDG 耦合方法的最优阶一致收敛性分析

谢胜兰, 祝鹏   

  1. 嘉兴学院数理与信息工程学院, 浙江嘉兴 314001
  • 收稿日期:2013-09-25 出版日期:2014-09-15 发布日期:2014-09-30
  • 基金资助:

    浙江省自然科学基金项目(LQ12A01014)和浙江省教育厅科研项目(Y201330020)资助.

谢胜兰, 祝鹏. 奇异摄动问题 FEM/LDG 耦合方法的最优阶一致收敛性分析[J]. 数值计算与计算机应用, 2014, 35(3): 189-205.

Xie Shenglan, Zhu Peng. UNIFORMLY CONVERGENT HIGHER ORDER FEM/LDG COUPLED METHOD FOR SOLVING SINGULARLY PERTURBED PROBLEM ON BAKHVALOV-SHISHKIN MESH[J]. Journal of Numerical Methods and Computer Applications, 2014, 35(3): 189-205.

UNIFORMLY CONVERGENT HIGHER ORDER FEM/LDG COUPLED METHOD FOR SOLVING SINGULARLY PERTURBED PROBLEM ON BAKHVALOV-SHISHKIN MESH

Xie Shenglan, Zhu Peng   

  1. School of Math-Physics and Information Engineering, Jiaxing University, Jiaxing 314001, Zhejiang, China
  • Received:2013-09-25 Online:2014-09-15 Published:2014-09-30
本文在 Bakhvalov-Shishkin 网格上分析了采用高次元的 FEM/LDG 耦合方法求解一维对流扩散型奇异摄动问题的最优阶一致收敛性. 取kk≥1)次分片多项式和网格剖分单元数为N时, 在能量范数度量下, Bakhvalov-Shishkin 网格上可获得ON-k)的一致误差估计. 在数值算例部分对理论分析结果进行了验证.
In this paper, we propose and analyze a higher order FEM/LDG coupled method for solving singularly perturbed convection-diffusion problem. Based on piecewise polynomial approximations of degree k(k≥1), a uniform convergence rate O(N-k) in associated norm is established on Bakhvalov-Shishkin mesh, where $N$ is the number of elements. Numerical experiments complement the theoretical results.

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[1] 尹云辉, 祝鹏, 杨宇博. 奇异摄动问题在Bakhvalov-Shishkin网格上的有限元超收敛[J]. 数值计算与计算机应用, 2013, 34(4): 257-265.
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