On the convergence of finite difference scheme for elliptic equation with coefficients containing Dirac distribution

Abstract

First boundary value problem for elliptic equation with youngest coefficient containing Dirac distribution concentrated on a smooth curve is considered. For this problem a finite difference scheme on a special quasiregular grid is constructed. The finite difference scheme converges in discrete $W_2^1$ norm with the rate $O(h^{3/2})$. Convergence rate is compatible with the smoothness of input data.