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Nonconforming mixed finite element method for the stationary conduction-convection problem. (English) Zbl 1165.65080
The Boussinnesq approximation of the Navier-Stokes equation for the velocity and the pressure is coupled with the convection-diffusion equation for the temperature. Rectangular finite elements are chosen. The velocity is modeled by a nonconforming element of Crouzeix-Raviart type with the nodal basis functions $$\{1,\xi,\eta,\eta^2\}$$ and$$\{1,\xi,\eta,\xi^2\}$$ for its two components. The convergence analysis is performed by error estimates in a broken $$H^1$$-norm for the velocity, $$L^2$$-norm for the pressure, and $$H^1$$-seminorm for the temperature

##### MSC:
 65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs 65N15 Error bounds for boundary value problems involving PDEs 76D05 Navier-Stokes equations for incompressible viscous fluids 76M10 Finite element methods applied to problems in fluid mechanics 65N12 Stability and convergence of numerical methods for boundary value problems involving PDEs 35Q30 Navier-Stokes equations
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