A posteriori error analysis for a transient conjugate heat transfer problem

We consider the accuracy of an operator decomposition finite element method for a transient conjugate heat transfer problem consisting of two materials coupled through a common boundary. We derive accurate a posteriori error estimates that account for the transfer of error between components of the operator decomposition method as well as the errors in solving the iterative system. We address a loss of order of convergence that results from the decomposition, and show that the order of convergence is limited by the accuracy of the transferred gradient information. We extend a boundary flux recovery method to transient problems and use it to regain the expected order of accuracy in an efficient manner. In addition, we use the a posteriori error estimates to adaptively compute the recovered boundary flux only within the domain of dependence for a quantity of interest.