Numerical Solution of a Two-Dimensional Parabolic Transmission Problem
Keywords:
Transmission problem, initial-boundary value problem, disconnected domains, Sobolev spaces, finite differences, convergence rate.Abstract
An initial boundary value problem for a two-dimensional parabolic equation in two disconnected rectangles is investigated. 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 logarithmic factor of the mesh-size), is obtained.