A general procedure for deriving stabilized space–time finite element methods for advective–diffusive problems

Published in International Journal for Numerical Methods in Fluids Vol. 31 (1), pp. 203-221, 1999
DOI: 10.1002/(SICI)1097-0363(19990915)31:1<203::AID-FLD964>3.0.CO;2-Z

Abstract

A procedure to derive stabilized space–time finite element methods for advective–diffusive problems is presented. The starting point is the stabilized balance equation for the transient case derived by Oñate [Comput. Methods Appl. Mech. Eng., 151, 233–267 (1998)] using a finite increment calculus approach. A description of the new stabilization method and a procedure for computing the stabilization parameter of the space–time solution is given. The efficiency of the stabilization approach is shown in the solution of some transient advective–diffusive problems, including the non‐linear Burger's equation