A stable second-order accurate, finite element scheme for the analysis of two-dimensional incompressible viscous flows

Two types of elements are candidates for optimal reduced integration penalty methods: the Q(2) element for velocities with discontinuous piecewise linear pressures, presently designated the Q(2)/P(1) method, and the 8-node isoparametric element with discontinuous piecewise linear pressures, designated the I(8)/P(1) element. Attention is given to the circumstances under which the former satisfies the LBB condition. It is found that the Q(2)/P(1) element is stable, and exhibits an optimal convergence rate. Ways are suggested of making the I(8)/P(1) element stable for certain problem classes.