## A coupled Newton iterative mixed finite element method for stationary conduction-convection problems.(English)Zbl 1206.65249

The authors give a coupled Newton iterative mixed finite element method (MFEM) for solving stationary conduction-convection problems in two dimension. For solving the equations of conduction-convection problems, they use the Newton iterative MFEM. They derive a stability and convergence analysis in the $$H ^{1}$$-norm of $${u_h^n, T_h^n}$$ and the $$L ^{2}$$-norm of $${p_h^n}.$$ They prove that their method is stable and has a good precision. They also give some numerical results, which prove that the coupled Newton iterative MFEM is highly efficient for stationary conduction-convection problems.

### MSC:

 65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs 65N12 Stability and convergence of numerical methods for boundary value problems involving PDEs 35J65 Nonlinear boundary value problems for linear elliptic equations 65N15 Error bounds for boundary value problems involving PDEs
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