Simple \(C^ 0\) approximations for the computation of incompressible flows (Q1093452)

We study various regularization procedures accomodating the P1-P1 and Q1- Q1 discretization of the 2D Stokes problem. The results are, in the P1-P1 case, compared with those obtained with a simple stable P1 element, namely the mini element. It is shown that the use of the latter is in fact equivalent to a regularization method. Finally, the practical importance of consistency is discussed and a new formulation is proposed to enforce that condition even in the P1-P1 case.