Semi-discrete error estimates of the evolutionary Stokes equations with inhomogeneous Dirichlet boundary data

This work concerns finite element analysis of the evolutionary Stokes equation with inhomogeneous Dirichlet boundary data. The Dirichlet boundary data are enforced using a Lagrange multiplier approach generalized from the work of Gunzburger and Hou (1992) for the steady Stokes equations. With a practical choice of finite element spaces, the computation of the Lagrange multiplier-the boundary stress-is uncoupled from that of the velocity and the pressure. Various semi-discrete (in space) error estimates are presented for the velocity, pressure and the Lagrange multiplier.