| 奇异摄动问题的LDG／FEM耦合解法 |
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| 引用本文： | 祝鹏,谢胜兰. 奇异摄动问题的LDG／FEM耦合解法[J]. 嘉兴学院学报, 2011, 23(6): 5-11. DOI: 10.3969/i.issn.1008-6781.2011.06.001 |
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| 作者姓名： | 祝鹏 谢胜兰 |
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| 作者单位： | 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： | 嘉兴学院科研启动基金,嘉兴学院重点科研课题资助项目 |
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| 摘 要： | 根据奇异摄动问题解的特点,提出了一种求解奇异摄动问题的新方法——LDG／FEM耦合方法．该方法将计算区域分为两个不重叠的子区域,在解变化较大的区域采用具有较好稳定性的间断有限元方法,在解变化平缓的区域采用自由度较少的连续有限元方法．证明了该耦舍方法导出的离散系统的解的存在性和唯一性,并证明了该方法的稳定性．数值结果表明：LDG／FEM耦合方法在Shishkin网格上是一致收敛的．
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| 关 键 词： | 奇异摄动问题 间断有限元 连续有限元 Shishkin网格 LDG／FEM耦合方法 |
A LDG/FEM Coupled Method for Singular Perturbation Problem |
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| ZHU Peng,XE Sheng-lan. A LDG/FEM Coupled Method for Singular Perturbation Problem[J]. Journal of Jiaxing College, 2011, 23(6): 5-11. DOI: 10.3969/i.issn.1008-6781.2011.06.001 |
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| Authors: | ZHU Peng XE Sheng-lan |
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| Affiliation: | ZHU Peng,XIE Sheng-lan(School of Mathematics,Physics and Information Engineering,Jiaxing University,Jiaxing,Zhejiang 314001) |
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| Abstract: | Based on the characteristic of solutions to the singular perturbation problems,this paper purposes a new method,LDG/FEM coupled method,for solving the problems.The basic idea of this new method is to split the domain into two disjoint subdomains.Taking into account the advantages of the LDG and FEM methods,we adopt the LDG in the subdomain where the solution varies rapidly while the FEM in the other subdomain due to its lower computational cost.The existence and uniqueness of the numerical solution,the stab... |
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| Keywords: | singular perturbation problem discontinuous finite element continuous finite element Shishkin mesh LDG/FEM coupled method |
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