A pressure-Poisson stabilized finite element method for the non-stationary Stokes equations to circumvent the inf–sup condition

摘要

In this article, stabilized finite element methods are considered for the non-stationary Stokes equations, based on some lowest equal-order finite elements space pair (Xh, Mh) which do not satisfy the discrete inf–sup condition. The stability of two kinds of methods is derived under some regularity assumptions. Then, the convergence of the penalty method and the pressure-Poisson stabilized method is compared. The result shows that the former error limits the order of approximation to O(ϵ+h/ϵ), and the latter yields the optimal error estimate O(h).