Year: 2010
Author: C.-Y. Jung, R. Temam
International Journal of Numerical Analysis and Modeling, Vol. 7 (2010), Iss. 3 : pp. 462–476
Abstract
Continuing an earlier work in space dimension one, the aim of this article is to present, in space dimension two, a novel method to approximate stiff problems using a combination of (relatively easy) analytical methods and finite volume discretization. The stiffness is caused by a small parameter in the equation which introduces ordinary and corner boundary layers along the boundaries of a two-dimensional rectangle domain. Incorporating in the finite volume space the boundary layer correctors, which are explicitly found by analysis, the boundary layer singularities are absorbed and thus uniform meshes can be preferably used. Using the central difference scheme at the volume interfaces, the proposed scheme finally appears to be an efficient second-order accurate one.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/2010-IJNAM-731
International Journal of Numerical Analysis and Modeling, Vol. 7 (2010), Iss. 3 : pp. 462–476
Published online: 2010-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 15
Keywords: Finite volume methods boundary layers correctors asymptotic analysis singularly perturbed problems stiff problems.