期刊
JOURNAL OF SCIENTIFIC COMPUTING
卷 36, 期 2, 页码 243-261出版社
SPRINGER/PLENUM PUBLISHERS
DOI: 10.1007/s10915-008-9187-7
关键词
tailored finite point method; singular perturbation problem; unbounded domain; artificial boundary condition
资金
- NSFC [10471073, 10301017, 10676017]
- National Basic Research Program of China [2005CB321701]
- National University of Ireland, Cork
- Science Foundation Ireland [04/BR/M0055, 04/BR/M0055s1]
- Science Foundation Ireland (SFI) [04/BR/M0055, 04/BR/M0055s1] Funding Source: Science Foundation Ireland (SFI)
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 epsilon. In the contrast, the traditional finite element method does not get satisfactory numerical results with the same mesh.
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