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Zbl 1203.65221
Han, Houde; Huang, Zhongyi; Kellogg, R.Bruce
A tailored finite point method for a singular perturbation problem on an unbounded domain.
(English)
[J] J. Sci. Comput. 36, No. 2, 243-261 (2008). ISSN 0885-7474; ISSN 1573-7691/e

Summary: 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, H.D.: The artificial boundary method - numerical solutions of partial differential equations on unbounded domains. In: Li, T., Zhang, P. (eds.) Frontiers and Prospects of Contemporary Applied Mathematics. Higher Education Press, World Scientific (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.
MSC 2000:
*65N06 Finite difference methods (BVP of PDE)

Keywords: tailored finite point method; singular perturbation problem; unbounded domain; artificial boundary condition

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