A modification of the least-squares stabilization for the Stokes equations

We present a new variant of the classical weighted least-squares stabilization for the Stokes equations. Compared to the original formulation, the new method has improved accuracy properties, especially near boundaries. Furthermore, the new discretization does not need modification of the right hand side, which makes it easier to implement for more complicated equations. For higher order polynomials, the constants in the stability estimate do not deteriorate as in the original method making it more attractive. Our approach is based on local projections of the residual terms which are used in order to achieve consistency of the method, avoiding local evaluation of the strong form of the differential operator. We give a priori and a posteriori estimates. We also show convergence of a simple iterative method which uses a solver for the original stabilized discretization as preconditioner. Numerical experiments indicate that the presented approach is at least as accurate as the original method, but offers some algorithmic advantages. The ideas presented here also apply to the nonstationary Navier-Stokes equations. This is the topic of a forthcoming work. (orig.)SIGLEAvailable from TIB Hannover: RR 1606(2000,4) / FIZ - Fachinformationszzentrum Karlsruhe / TIB - Technische InformationsbibliothekDEGerman