Error analysis of some finite element methods for the Stokes problem

Source abstract

We prove the optimal order of convergence for some two-dimensional finite element methods for the Stokes equations. First we consider methods of the Taylor-Hood type: the triangular P 3 − P 2 {P_3} - {P_2} element and the Q k − Q k − 1 , {Q_k} - {Q_{k - 1}}, , k ≥ 2 k \geq 2 , family of quadrilateral elements. Then we introduce two new low-order methods with piecewise constant approximations for the pressure. The analysis is performed using our macroelement technique, which is reviewed in a slightly altered form.