A coupled Newton iterative mixed finite element method for stationary conduction–convection problems

In this paper, a coupled Newton iterative mixed finite element method (MFEM) for solving the stationary conduction–convection problems in two dimension is given. In our method, the Newton iterative MFEM is used for solving all the equations of the conduction–convection problems. The stability and convergence analysis in H1-norm of $${u_h^n, T_h^n}$$ and the L2-norm of $${p_h^n}$$ are derived. The theory analysis shows that our method is stable and have a good precision. Some numerical results are also given, which show that the coupled Newton iterative MFEM is highly efficient for the stationary conduction–convection problems.

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