The penalty method applied to the instationary stokes equations

Abstract

A mathematical analysis of the penalty method applied to the initial boundary value problem for the Stokes equations is presented. We prove a regularity result for the penalty equations by means of a spectral Galerkin method. Based upon this result the discretization in time (by a multistep integration formula) and in space (by a finite element method) is shown to give an optimal L ²-error estimate.

Additional information

Notes on contributors

F.-K. Hebeker

M. Crouzeix