Convergence analysis of coupling iterations for the unsteady transmission problem with mixed discretizations
We analyze the convergence rate of the Dirichlet-Neumann iteration for the fully discretized one dimensional unsteady transmission problem. Specifically, we consider the coupling of two linear heat equations on two identical non overlapping intervals. The Laplacian is discretized using finite differences on one interval and finite elements on the other and the implicit Euler method is used for the