The deterioration occurs due to a consistency error associated with the boundary layer - we show how a modification of the elements at the boundary can fix the problem. This scheme is based on the decoupled computation of the new velocity-field and pressure iterates by means of Chorin's projection method. Second, a thorough analysis of this scheme is given that leads to optimal error statements which apply to general flow situations. The representation used involves only single and double layer potentials and does not require the discretization of the hypersingular integral operator as in the symmetric formulation. The stability of the hybrid Galerkin discretization is based on a BBL- like stability condition for the trial spaces.
Numerical examples confirm the theoretical results.
An instrumental ingredient is a new interpolation operator which requires minimal regularity, exhibits optimal approximation properties and preserves positivity. Both upper and lower bounds are proved and their optimality is explored with several examples. Sharp a priori bounds for the a posteriori estimators are given, and extensions of the results to double obstacle problems are briefly discussed. The domain is approximated by a polyhedron and a numerical integration is taken into account. Using Fourier decomposition, we define weighted Sobolev spaces of solution and we prove expected regularity results.