A defect–correction parameter-uniform numerical method for a singularly perturbed convection–diffusion problem in one dimension
A defect–correction parameter-uniform numerical method for a singularly perturbed convection–diffusion problem in one dimension
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DOI：
10.1007/s11075-006-9021-y
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发表时间：
2006-04
影响因子：
2.1
通讯作者：
J. Gracia;E. O'Riordan
中科院分区：
文献类型：
--
作者：
J. Gracia;E. O'Riordan
利用缺陷修正原理，可以设计求解奇异摄动微分方程的单调二阶参数鲁棒数值方法。然而，二阶参数一致收敛的证明可能是困难的，即使在一维。在本文中，我们研究了标准缺陷纠正方案的一个变体。提出此变体是为了简化一维对流扩散问题中缺陷校正方法的分析。数值结果验证了理论分析的正确性。
Monotone second order parameter-robust numerical methods for singularly perturbed differential equations can be designed using the principles of defect-correction. However, the proofs of second order parameter-uniform convergence can be difficult, even in one dimension. In this paper, we examine a variant of the standard defect-correction scheme. This variant is proposed in order to simplify the analysis of a defect-correction method in the case of a one dimensional convection–diffusion problem. Numerical results are presented to validate the theoretical results.