Modified cross-grid finite elements for the Stokes problem

Abstract

The stability of modified cross-grid elements for the approximation of the Stokes problem using continuous piecewise linear polynomials to approximate velocities and piecewise constants to approximate pressures is proved. A key feature of the method is that the mesh for pressure is modified so that the method is stable without augmenting pressure jumps. A numerical test which confirms the stability and the optimal order error estimate is presented. (C) 2002 Elsevier Science Ltd. All rights reserved.