Givi Berikelashvili and Bidzina Midodashvili
abstract:
A mixed problem with the third kind condition on one part of boundary and with
the Dirichlet condition on the rest part of the boundary formulated for the
Poisson equation, is considered in a unit square. To obtain an approximate
solution, we suggest the two-stage finite-difference correction method. It is
proved that the solution of the corrected scheme converges at the rate $O(h^m)$
in the discrete $L_2$-norm, when the solution of the initial problem belongs to
the Sobolev space $W_2^m(\Omega)$ with exponent $m\in (2,4]$.
Mathematics Subject Classification: 65N06, 65N12
Key words and phrases: Difference scheme, method of corrections, improvement of accuracy, compatible estimates of convergence rate