Domain decomposition of constrained optimal control problems for 2d elliptic system on networked domains: convergence and a posteriori error estimates - Leugering, Günter (2008)
We consider optimal control problems for elliptic systems under control constraints on networked domains. In particular, we study such systems in a format that allows for applications in problems including membranes and Reissner-Mindlin plates on multi-link-domains, called networks. We first provide the models, derive first order optimality conditions in terms of variational equations and inequalities for a control-constrained linear-quadratic optimal control problem, and then introduce a non-overlapping iterative domain decomposition method, which is based on Robin-type interface updates at multiple joints (edges). We prove convergence of the iteration and derive a posteriori error estimates with respect to the iteration across the interfaces.