A nonconforming finite element method of streamline diffusion type for the incompressible Navier-Stokes equations. (English) Zbl 0699.76032
Summary: A nonconforming finite element method of streamline diffusion type for solving the stationary and incompressible Navier-Stokes equations is considered. Velocity field and pressure field are approximated by piecewise linear and piecewise constant functions, respectively. The existence of solutions of the discrete problem and the strong convergence of a subsequence of discrete solutions are established. Error estimates are presented for the uniqueness case.
MSC:
76D05 | Navier-Stokes equations for incompressible viscous fluids |
65N30 | Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs |
76R99 | Diffusion and convection |