variavel0=Lucia Catabriga - luciac@inf.ufes.br UFES Alvaro Luiz Gayoso de Azeredo Coutinho - alvaro@nacad.ufrj.br COPPE/UFRJ Tayfun E Tezduyar - tezduyar@rice.edu Rice University Abstract. We present, for the SUPG formulation of inviscid compressible flows, stabilization parameters defined based on the element-level matrices. These definitions are expressed in terms of the ratios of the norms of the relevant matrices. They take into account the flow field, the local length scales, and the time step size. We compare the performance of these stabilization parameters, accompanied by a shock-capturing parameter. We investigate the performance difference between updating the stabilization and shock-capturing parameter at the end of every time step and at the end of every nonlinear iteration within a time step. We also investigate the influence of activating na agorithmic option that was introduced earlier; which is based on freezing the shock-capturing parameter at its current value when a convergence stagnation is detected. Keywords. Euler equations, compressible flow, finite elements, element-by-element data structures, stabilization parameter.