Stable nonconforming methods or the Stokes problem

It is the purpose of this paper to show that the mixed finite element scheme with pressure stabilization for the Stokes problem converges with an optimal order for some higher order nonconforming triangular elements. Specifically an optimal order convergence is given for the NCP4-P-3 element using nonconforming piecewise quartic velocities paired with discontinuous piecewise cubic pressures. The NCP6-P-5 element is analyzed similarly. To verify the stability condition and the error estimates for nonconforming elements, we combine the ideas of macroelement technique of Stenberg and the arguments for Galerkin least squares methods. (C) 2000 Elsevier Science Inc. All rights reserved.