Stability and convergence of difference schemes for parabolic interface problems

In this paper we report results on stability and convergence of twolevel difference schemes for parabolic interface equations. Energy norms that rely on spectral problems containing the eigenvalue in boundary conditions or in conditions on conjugation are introduced. Necessary and sufficient stability conditions in these norms for weighted difference schemes are established. Convergence rate estimates of difference schemes compatible with the smoothness of the differential problems solutions are presented. The introducing of intrinsic discrete norms enable us to precise the values of the mesh steps that control stability and the rate of convergence of the difference schemes.