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

Si, Zhiyong; He, Yinnian

Computing 89, No. 1-2, 1-25 (2010).

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.

Reviewer: Yaşar Sözen (Istanbul)

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

Keywords:

Boussinesq approximation; mixed finite element method; coupled Newton iterative; stability analysis; error estimates; stationary conduction-convection problems

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