Solutions of 3D Navier–Stokes benchmark problems with adaptive finite elements

This paper presents a numerical study of 3D Navier–Stokes benchmark problems defined within the DFG high-priority research program in 1996. Specifically, we investigate the accuracy of an equal-order finite element method based on piecewise quadratic shape functions with local projections stabilization on locally refined meshes for stationary laminar flows around an obstacle with circular and square cross-section. It turns out that on globally refined meshes the new stabilization method is comparable to Q2/P1disc element which was the best one in recent investigations of John [Int J Numer Math Fluids 2002;40:775–98]. Furthermore, on locally refined meshes we are able to produce reference values for the geometry with singularities (square cross-section) which were still unknown up to now.