Abstract

In this paper, we investigate an elliptic transmission problem in disjoint domains. A priori estimate for its weak solution in appropriate Sobolev-like space is proved. A finite difference scheme approximating this problem is proposed and analyzed. An estimate of the convergence rate, compatible with the smoothness of the input data (up to a slowly increasing logarithmic factor of the mesh size), is obtained.

Keywords: Elliptic transmission problem; disjoint domains; Sobolev-like space.

MSC: 65N12, 65N15

Pages:  418$-$429     

Volume  66 ,  Issue  4 ,  2014