A least squares Galerkin-Petrov nonconforming mixed finite element method for the stationary Conduction-Convection problem

In this paper, a least squares Galerkin-Petrov nonconforming mixed finite element method (LSGPNMFM) is proposed and analyzed for the stationary Conduction-Convection problem. We use P2-nonconforming as approximation space for the velocity, the linear element for the pressure space and the quadratic element for the temperature space. The mixed finite element spaces Xh and Mh need not satisfy inf-sup condition, the existence, uniqueness and convergence of the discrete solution are presented and error estimates of optimal order are derived in the case of sufficient viscosity.