A posteriori analysis of operator decomposition on interface problems

Abstract

This thesis is devoted to the a posteriori analysis of the effects of operator decomposition on interface problems. Operator decomposition offers an attractive solution strategy for multi-physics and multi-scale problems. This technique allows previously defined component codes optimized for single physics problems to be reused in an iterative manner to solve a multi-physics, multi-scale problem. This is also called loose-coupling or a partitioned approach. Unfortunately, this technique introduces additional errors due to the transfer of information between components. For interface problems, this results in a loss of accuracy for the converged approximation in the L2 norm. In this thesis, we use a posteriori analysis to detect the source of this loss of accuracy and show that a common flux recovery technique can be used to recovery the expected accuracy.