On the convergence rate of a difference solution of the Poisson equation with fully nonlocal constraints | Zendy

Givi Berikelashvilia | Zendy; Nodar Khomeriki | Zendy

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On the convergence rate of a difference solution of the Poisson equation with fully nonlocal constraints

Author(s) -

Givi Berikelashvilia,

Nodar Khomeriki

Publication year - 2014

Publication title -

nonlinear analysis modelling and control

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.734

H-Index - 32

eISSN - 2335-8963

pISSN - 1392-5113

DOI - 10.15388/na.2014.3.4

Subject(s) - mathematics , sobolev space , discretization , convergence (economics) , rate of convergence , boundary value problem , poisson's equation , domain (mathematical analysis) , boundary (topology) , mathematical analysis , space (punctuation) , a priori and a posteriori , scheme (mathematics) , poisson distribution , order (exchange) , computer science , channel (broadcasting) , philosophy , statistics , epistemology , economics , economic growth , computer network , finance , operating system

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 . The corresponding finite-difference scheme is constructed on a mesh, which selection does not depend on the value . 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 orders (1 < s 6 3).

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