A Tailored Finite Point Method for a Singular Perturbation Problem on an Unbounded Domain
In this paper, we propose a tailored-finite-point method for a kind of singular perturbation problems in unbounded domains. First, we use the artificial boundary method (Han in Frontiers and Prospects of Contemporary Applied Mathematics, [ 2005 ]) to reduce the original problem to a problem on bound...
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| Published in | Journal of scientific computing Vol. 36; no. 2; pp. 243 - 261 |
|---|---|
| Main Authors | , , |
| Format | Journal Article |
| Language | English |
| Published |
Boston
Springer US
01.08.2008
Springer Nature B.V |
| Subjects | |
| Online Access | Get full text |
| ISSN | 0885-7474 1573-7691 |
| DOI | 10.1007/s10915-008-9187-7 |
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| Abstract | In this paper, we propose a tailored-finite-point method for a kind of singular perturbation problems in unbounded domains. First, we use the artificial boundary method (Han in Frontiers and Prospects of Contemporary Applied Mathematics, [
2005
]) to reduce the original problem to a problem on bounded computational domain. Then we propose a new approach to construct a discrete scheme for the reduced problem, where our finite point method has been tailored to some particular properties or solutions of the problem. From the numerical results, we find that our new methods can achieve very high accuracy with very coarse mesh even for very small
ε
. In the contrast, the traditional finite element method does not get satisfactory numerical results with the same mesh. |
|---|---|
| AbstractList | In this paper, we propose a tailored-finite-point method for a kind of singular perturbation problems in unbounded domains. First, we use the artificial boundary method (Han in Frontiers and Prospects of Contemporary Applied Mathematics, [2005]) to reduce the original problem to a problem on bounded computational domain. Then we propose a new approach to construct a discrete scheme for the reduced problem, where our finite point method has been tailored to some particular properties or solutions of the problem. From the numerical results, we find that our new methods can achieve very high accuracy with very coarse mesh even for very small Delta *e. In the contrast, the traditional finite element method does not get satisfactory numerical results with the same mesh. In this paper, we propose a tailored-finite-point method for a kind of singular perturbation problems in unbounded domains. First, we use the artificial boundary method (Han in Frontiers and Prospects of Contemporary Applied Mathematics, [2005]) to reduce the original problem to a problem on bounded computational domain. Then we propose a new approach to construct a discrete scheme for the reduced problem, where our finite point method has been tailored to some particular properties or solutions of the problem. From the numerical results, we find that our new methods can achieve very high accuracy with very coarse mesh even for very small ε. In the contrast, the traditional finite element method does not get satisfactory numerical results with the same mesh. In this paper, we propose a tailored-finite-point method for a kind of singular perturbation problems in unbounded domains. First, we use the artificial boundary method (Han in Frontiers and Prospects of Contemporary Applied Mathematics, [ 2005 ]) to reduce the original problem to a problem on bounded computational domain. Then we propose a new approach to construct a discrete scheme for the reduced problem, where our finite point method has been tailored to some particular properties or solutions of the problem. From the numerical results, we find that our new methods can achieve very high accuracy with very coarse mesh even for very small ε . In the contrast, the traditional finite element method does not get satisfactory numerical results with the same mesh. |
| Author | Han, Houde Huang, Zhongyi Kellogg, R. Bruce |
| Author_xml | – sequence: 1 givenname: Houde surname: Han fullname: Han, Houde organization: Dept. of Mathematical Sciences, Tsinghua University – sequence: 2 givenname: Zhongyi surname: Huang fullname: Huang, Zhongyi email: zhuang@math.tsinghua.edu.cn organization: Dept. of Mathematical Sciences, Tsinghua University – sequence: 3 givenname: R. Bruce surname: Kellogg fullname: Kellogg, R. Bruce organization: Department of Mathematics, University of South Carolina |
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| Cites_doi | 10.1002/fld.365 10.1016/S0045-7825(97)00329-0 10.1137/S0036142998341805 10.1002/(SICI)1097-0207(19961130)39:22<3839::AID-NME27>3.0.CO;2-R 10.1016/S0377-0427(96)00113-6 10.2307/2007596 10.1007/3-540-36487-0_44 10.1080/00036810601066574 10.1002/(SICI)1098-2426(199611)12:6<657::AID-NUM2>3.0.CO;2-R 10.1016/j.cma.2003.11.010 10.1007/BF01093706 10.1007/978-3-662-03206-0 10.1090/S0025-5718-1984-0736447-2 |
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| Keywords | Tailored finite point method Unbounded domain Singular perturbation problem Artificial boundary condition |
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| SubjectTerms | Accuracy Algorithms Applications of mathematics Boundaries Computation Computational Mathematics and Numerical Analysis Construction Finite element method Mathematical analysis Mathematical and Computational Engineering Mathematical and Computational Physics Mathematical models Mathematics Mathematics and Statistics Singular perturbation Theoretical |
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| Title | A Tailored Finite Point Method for a Singular Perturbation Problem on an Unbounded Domain |
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