A defect-correction mixed finite element method for stationary conduction-convection problems.

*(English)*Zbl 1204.76021Summary: A defect-correction mixed finite element method (MFEM) for solving the stationary conduction-convection problems in two-dimension is given. In this method, we solve the nonlinear equations with an added artificial viscosity term on a grid and correct this solution on the same grid using a linearized defect-correction technique. The stability is given and the error analysis in \(L^2\) and \(H^1\)-norm of \(u, T\) and the \(L^2\)-norm of \(p\) are derived. The theory analysis shows that our method is stable and has a good precision. Some numerical results are also given, which show that the defect-correction MFEM is highly efficient for the stationary conduction-convection problems.

##### MSC:

76M10 | Finite element methods applied to problems in fluid mechanics |

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\textit{Z. Si} and \textit{Y. He}, Math. Probl. Eng. 2011, Article ID 370192, 28 p. (2011; Zbl 1204.76021)

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