Numerical analysis of laminar flow over a step by a finite element method with divergence free elements

A standard Galerkin treatment is employed to discretize the incompressible Navier-Stokes equations for flow over a backward facing step. Additionally, divergence free test functions are devised for the weak solution to form a basis for explicitly defined divergence free extended quadratic conformal triangular elements with seven nodes. Pressure is treated as discontinuous over the element boundaries. The resulting velocity and stress values are provided, including values obtained using a penalty function in generating the divergence free elements. Temporally and spatially higher resolutions are shown to be available with the divergence free basis functions. The improvements over usage of a penalty function becomes apparent with a finer grid mesh.