The local solution behavior near corners formed by the intersection of a slip surface with either a no-slip or a shear-free boundary is analyzed by finite element calculations of the two-dimensional flow of an inertialess Newtonian fluid in several model flow geometries; these flows are the flow in a tapered contraction, a sudden expansion and the extrudate swell from a planar die. Local finite element mesh refinement based on irregular, embedded elements is used to obtain extremely fine resolution of the velocity and pressure fields near the region where there is a sudden change in boundary condition. The calculations accurately reproduce the expected asymptotic behavior for a shear-free surface intersecting a no-slip boundary, where the solution is given by a self-similar form for the velocity and pressure fields. Replacing the shear-free condition with a slip condition yields a similar form for the local velocity and pressure fields and indicates that the slip boundary behaves, to leading order, as a shear-free surface. Calculations for a slip boundary intersecting a shear-free surface yield similar results, with the local behavior being given by asymptotic analysis for two shear-free surfaces intersecting to form a wedge. These results suggest that replacing the no-slip boundary condition in planar Newtonian die swell with a slip boundary condition can give rise to local behavior of velocity gradients and pressure which ismore singularthan the flow created with no-slip boundary conditions. This prediction is confirmed by calculations of Newtonian die swell with slip. These calculations also demonstrate that the local solution in Newtonian die swell is sensitive to the details of the numerical method. ©1997 American Institute of Physics.