On the convergence of difference schemes for one nonlocal boundary-value problem

被引：10

作者：

Berikelashvili, Givi ^{[1
,2
]}

Khomeriki, Nodar ^{[2
]}

机构：

[1] I Javakhishvili Tbilisi State Univ, A Razmadze Math Inst, GE-0186 Tbilisi, Georgia

[2] Georgian Tech Univ, Dept Math, GE-0175 Tbilisi, Georgia

来源：

LITHUANIAN MATHEMATICAL JOURNAL | 2012年 / 52卷 / 04期

关键词：

Poisson equation; nonlocal integral conditions; finite-difference scheme; POISSON EQUATION;

D O I：

10.1007/s10986-012-9178-0

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We consider a nonlocal boundary-value problem for the Poisson equation in a rectangular domain. Dirichlet conditions are posed on a pair of adjacent sides of a rectangle, and integral constraints are given instead of standard boundary conditions on the other pair. The corresponding difference scheme is constructed and investigated; an a priori estimate of the solution is obtained with the help of energy inequality method. Discretization error estimate that is compatible with the smoothness of the solution sought is obtained.

引用

页码：353 / 362

页数：10

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