A sharp error estimate for the numerical solution of multivariate Dirichlet problems

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS

卷:75

Article

Anastassiou, GA ; Bendikov, A

关键词: primary, Dirichlet problem-continuous and discrete;    Wiener process and simple random walk, convergence with rates;    second modulus of continuity;    sharp inequality;    approximate solution;    secondary, average operator;    first exit time;    uniform grid;    Lipschitz class;    arbitrary domain;   

DOI  :  10.1016/S0377-0427(96)00052-0

来源: Elsevier

【 摘 要 】

For the multidimensional Dirichlet problem of the Poisson equation on an arbitrary compact domain, this study examines convergence properties with rates of approximate solutions, obtained by a standard difference scheme over inscribed uniform grids. Sharp quantitative estimates are given by the use of second moduli of continuity of the second single partial derivatives of the exact solution. This is achieved by employing the probabilistic method of simple random walk.

【 授权许可】

Free