  We consider the Dirichlet-Neumann iteration for partitioned simulation of
thermal fluid-structure interaction, also called conjugate heat transfer. We
analyze its convergence rate for two coupled fully discretized 1D linear heat
equations with jumps in the material coefficients across these. These are
discretized using implicit Euler in time, a finite element method on one
domain, a finite volume method on the other one and variable aspect ratio. We
provide an exact formula for the spectral radius of the iteration matrix. This
shows that for large time steps, the convergence rate is the aspect ratio times
the quotient of heat conductivities and that decreasing the time step will
improve the convergence rate. Numerical results confirm the analysis and show
that the 1D formula is a good estimator in 2D and even for nonlinear thermal
FSI applications.
