Burman, E; Santos, IP; (2017) Error estimates for transport problems with high Péclet number using a continuous dependence assumption. Journal of Computational and Applied Mathematics , 309 pp. 267-286. 10.1016/j.cam.2016.06.024.

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Abstract

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.

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