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A continuous interior penalty finite element method for steady-state natural convection problems. (Chinese. English summary) Zbl 1324.76034

Summary: In this paper, we propose a continuous interior penalty finite element method for solving steady-state natural convection problems. We add a stabilization term for having a \(L^2\)-control of the jump of the gradient of the velocity, temperature and pressure over element faces into the standard Galerkin formulation. The method can effectively solve instabilities due to the influence of dominating convection and the requirement of LBB condition, for mixed finite element spaces. Finally, a finite element error analysis of the problem is investigated and optimal error estimates for the velocity, temperature and pressure are established.

MSC:

76M10 Finite element methods applied to problems in fluid mechanics
65M60 Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs
76R10 Free convection
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