A balancing domain decomposition by constraints preconditioner for a hybridizable discontinuous Galerkin discretization of an elliptic optimal control problem

Abstract

We consider a hybridizable discontinuous Galerkin (HDG) method for an elliptic distributed optimal control problem and we propose a balancing domain decomposition by constraints (BDDC) preconditioner to solve the discretized system. We establish an error estimate of the HDG methods with explicit tracking of a regularization parameter ${\hat{I}}^2$. We observe that the BDDC preconditioner is robust with respect to ${\hat{I}}^2$. Numerical results are shown to support our findings.