On the convergence rate of a difference solution of the Poisson equation with fully nonlocal constraints
Articles
Givi Berikelashvilia
Tbilisi State University; Georgian Technical University,  Georgia
Nodar Khomeriki
Georgian Technical University, Georgia
Published 2014-10-30
https://doi.org/10.15388/NA.2014.3.4
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Keywords

integral conditions
energy inequalities
difference scheme
convergence rate

How to Cite

Berikelashvilia, G. and Khomeriki, N. (2014) “On the convergence rate of a difference solution of the Poisson equation with fully nonlocal constraints”, Nonlinear Analysis: Modelling and Control, 19(3), pp. 367–381. doi:10.15388/NA.2014.3.4.

Abstract

We consider the Poisson equation in a rectangular domain. Instead of the classical specification of boundary data, we impose an integral constraints on the inner stripe adjacent to boundary having the width ξ. The corresponding finite-difference scheme is constructed on a mesh, which selection does not depend on the value ξ. It is proved the unique solvability of the scheme. An a priori estimate of the discretization error is obtained with the help of energy inequality method. It is proved that the scheme is convergent with the convergence rate of order s-1, when the exact solution belongs to the fractional Sobolev space of order s (1<s ≤3).

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