Calculation of the advective limit of the SUPG stabilization parameter for linear and higher-order elements

We investigate, for linear and higher-order elements, various ways of calculating the advective limit of the stabilization parameter ("τ") used in the streamline-upwind/Petrov-Galerkin (SUPG) formulation of flow problems. In the context of a pure advection test problem, we compare the "UGN-based", element-matrix-based, and element-node-based calculations of the advective limit of the τ. Our investigation shows that the performances of the "UGN-based" and element-matrix-based τ definitions are comparable, with the element-matrix-based definition yielding somewhat lower τ values. We also show that for both definitions, as the polynomial orders increase, the τ values decrease, as they should.