A posteriori error estimation and adaptive mesh refinement for a multiscale operator decomposition approach to fluid-solid heat transfer

Authors:
Donald Estep;Simon Tavener;Tim Wildey
Affiliations:
Department of Mathematics and Department of Statistics, Colorado State University, Fort Collins, CO 80523-1874, USA;Department of Mathematics, Colorado State University, Fort Collins, CO 80523-1874, USA;The Institute for Computational Engineering and Sciences, The University of Texas, Austin, TX 78712, USA
Venue:
Journal of Computational Physics
Year:
2010

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Abstract

We analyze a multiscale 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 all sources of error, and in particular the transfer of error between fluid and solid domains. We use these estimates to guide adaptive mesh refinement. In addition, we provide compelling numerical evidence that the order of convergence of the operator decomposition method is limited by the accuracy of the transferred gradient information, and adapt a so-called boundary flux recovery method developed for elliptic problems in order to regain the optimal order of accuracy in an efficient manner. In an appendix, we provide an argument that explains the numerical results provided sufficient smoothness is assumed.