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A posteriori analysis and improved accuracy for an operator decomposition solution of a conjugate heat transfer problem. (English) Zbl 1176.65124

Authors’ summary: 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.

MSC:

65N15 Error bounds for boundary value problems involving PDEs
65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
35J25 Boundary value problems for second-order elliptic equations
65N50 Mesh generation, refinement, and adaptive methods for boundary value problems involving PDEs
65N55 Multigrid methods; domain decomposition for boundary value problems involving PDEs
80A20 Heat and mass transfer, heat flow (MSC2010)
80M10 Finite element, Galerkin and related methods applied to problems in thermodynamics and heat transfer
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