Abstract
We consider a nonlocal boundary-value problem for the Poisson equation in a rectangular domain. Dirichlet and Neumann conditions are posed on a pair of adjacent sides of a rectangle, and integral constraints are given instead of 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.
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Berikelashvili, G., Khomeriki, N. On a numerical solution of one nonlocal boundary-value problem with mixed Dirichlet–Neumann conditions. Lith Math J 53, 367–380 (2013). https://doi.org/10.1007/s10986-013-9214-8
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DOI: https://doi.org/10.1007/s10986-013-9214-8