SUPG stabilization parameters calculated from the quadrature-point components of the element-level matrices

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" and element-matrix-based calculations and the calculations from the quadrature-point components of the element-level matrices. Our investigation shows that the performances of all three definitions are comparable, with the element-based definitions yielding somewhat lower τ values and the quadrature-point-based definitions somewhat higher. We also show that for both the element-based and quadrature-point-based definitions, as the polynomial orders increase, the τ values decrease, as they should.