Error estimates for transport problems with high Péclet number using a continuous dependence assumption

摘要

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 holds 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 Burman (2014). 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.