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Multiphysics, multiscale models present signiflcant challenges in terms of computing accurate solutions and for estimating the error in information computed from numerical solutions. In this paper, we describe recent advances in extending the techniques of a posteriori error analysis to multiscale operator decomposition solution methods. While the particulars of the analysis vary considerably with the problem, there are several key ideas underlaying a general approach to treat operator decomposition multiscale methods that is underdevelopment. We explain these ideas in the context of three speciflc examples. 1. Multiscale, multiphysics problems Multiphysics, multiscale models that couple difierent physical processes interacting across a wide range of scales abound in the application areas of the SCIDAC program. Such models present signiflcant challenges for computing accurate numerical solutions, which makes it very important to obtain accurate estimates of error in computed information. But, multiphysics, multiscale problems also raise signiflcant challenges for error estimation. In this paper, we describe recent advances in computing a posteriori error estimates for multiscale operator decomposition, which is a powerful solution method for multiphysics, multiscale problems that is in widespread use in high performance computing.

A posteriori error analysis of multiscale operator decomposition methods for multiphysics models