The streamline-diffusion method of the lowest order nonconforming rectangular finite element is proposed for convection-diffusion problem. By making full use of the element＇s special property, the same convergence order as the previous literature is obtained. In which, the jump terms on the boundary are added to bilinear form with simple user-chosen parameter δKwhich has nothing to do with perturbation parameter εappeared in the problem under considered, the subdivision mesh size hKand the inverse estimate coefficient μin finite element space.
In this paper, a nonconforming triangular mixed finite element scheme with second order convergence behavior is proposed for the stationary Navier-Stokes equations.The new nonconforming triangular element is taken as approximation space for the velocity and the linear element for the pressure. The convergence analysis is presented and optimal error estimates of both broken H^1-norm and L^2-norm for velocity as well as the L^2-norm for the pressure are derived.
