AbstractThis paper develops a posteriori estimates for domain decomposition
methods with optimized Robin transmission conditions on the interface between
subdomains. We choose to demonstrate the methodology for mixed formulations,
with a lowest-order Raviart–Thomas–Nédélec discretization, often used
for heterogeneous and anisotropic porous media diffusion problems. Our
estimators allow to distinguish the spatial discretization and the domain
decomposition error components. We propose an adaptive domain decomposition
algorithm wherein the iterations are stopped when the domain decomposition
error does not affect significantly the overall error. Two main goals are
thus achieved. First, a guaranteed bound on the overall error is obtained at
each step of the domain decomposition algorithm. Second, important savings in
terms of the number of domain decomposition iterations can be realized.
Numerical experiments illustrate the efficiency of our estimates and the
performance of the adaptive stopping criteria.