Uniform convergence analysis of finite difference approximations for singular perturbation problems on an adapted grid

被引：23
作者：
Yanping Chen
机构：
[1] Xiangtan University,Department of Mathematics
来源：
Advances in Computational Mathematics | 2006年 / 24卷
关键词：
singular perturbation; moving mesh; rate of convergence; error estimate;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
A singularly perturbed two-point boundary value problem with an exponential boundary layer is solved numerically by using an adaptive grid method. The mesh is constructed adaptively by equidistributing a monitor function based on the arc-length of the approximated solutions. A first-order rate of convergence, independent of the perturbation parameter, is established by using the theory of the discrete Green's function. Unlike some previous analysis for the fully discretized approach, the present problem does not require the conservative form of the underlying boundary value problem.
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页码：197 / 212
页数：15
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