Investigation of the Stabilization Parameters of the Stabilized Finite Element Formulations

Abstract

The Team for Advanced Flow Simulation and Modeling at Rice University specializes in finite element computation of complex problems, relying on stabilized formulations such as the streamline-upwind/Petrov-Galerkin and pressure-stabilizing/PetrovGalerkin methods. These stabilization methods involve a stabilization parameter, T. Alternatives to the currently-used T definitions were provided in terms of element-level matrices and vectors. An extensive investigation of these stabilization parameters is performed with comparison to currently-used T definitions to determine their performance. Numerical data is reported to evaluate the behavior of these alternative stabilization parameters with changing element size, type, and distortion. This is accomplished through evaluation of the matrix-assembly outcome and test computations, with focus on boundary layer behavior. Test calculations are carried out in the context of a time-dependent advection-diffusion equation and the N avier-Stokes equations of incompressible flows, for both the semi-discrete formulation and the Deforming-Spatial-Domain/Stabilized Space-Time method.