Difference schemes for the dirichlet problem for an elliptical equation with discontinuous coefficients in an arbitrary region on a regular grid

Exact difference scheme operators are used to construct a difference scheme for a second-order elliptical equation with discontinuous coefficients. The solution of the scheme converges to the solution of the original problem at a rate O(h^1/2) in the grid norm W₂¹().Translated from Vychislitel'naya i Prikladnaya Matematika, No. 56, pp. 3–7, 1985