A Posteriori Analysis and Improved Accuracy for an Operator Decomposition Solution of a Conjugate Heat Transfer Problem

Abstract

We consider the accuracy of an operator decomposition finite element method for a 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 differences between the adjoints of the full problem and the discrete iterative system. We use these estimates to guide adaptive mesh refinement. In addition, 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 employ a boundary flux recovery method to regain the expected order of accuracy in an efficient manner.