Operator decomposition methods are an attractive solution strategy for computing complex phenomena involving multiple physical processes, multiple scales or multiple domains. The general strategy is to decompose the problem into components involving simpler physics over a relatively limited range of scales, and then to seek the solution of the entire system through an iterative procedure involving solutions of the individual components.
We analyze the accuracy of an operator decomposition finite element method for a conjugate heat transfer problem consisting of a fluid and a solid coupled through a common boundary. We derive accurate a posteriori error estimates that account for both local discretization errors and the transfer of error between fluid and solid domains. We use these estimates to guide adaptive mesh refinement. In addition, we show that the order of convergence of the operator decomposition method is limited by the accuracy of the transferred gradient information, and how a simple boundary flux recovery method can be used to regain the optimal order of accuracy in an efficient manner.
This is joint work with Don Estep and Tim Wildey, Department of Mathematics, Colorado State University.
