In this paper we discuss the behavior of stabilized finite element methods for the transient advection-diffusion problem with dominant advection and rough data. We show that provided a certain continuous dependence result hold for the quantity of interest, independent of the Péclet number, this quantity may be computed using a stabilized finite element method in all flow regimes. As an example of a stable quantity we consider the parameterized weak norm introduced in [2]. The same results may not be obtained using a standard Galerkin method. We consider the following stabilized methods: Continuous Interior Penalty (CIP) and Streamline Upwind Petrov-Galerkin (SUPG). The theoretical results are illustrated by computations on a scalar transport equation with no diffusion term, rough data and strongly varying velocity field.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.