An error estimate for two-dimensional Stokes driven cavity flow

Discontinuous velocity boundary data for the lid driven cavity flow has long been causing difficulties in both theoretical analysis and numerical simulations. In finite element methods, the variational form for the driven cavity flow is not valid since the velocity is not in H. Hence standard error estimates do not work. By using only W1,r (1 < r < 2) regularity and constructing a continuous approximation to the boundary data, here we present error estimates for both the velocity-pressure formulation and the pseudostressvelocity formulation of the two-dimensional Stokes driven cavity flow.