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

详细信息    查看全文

• 作者：Erik Burman^a ; ^{e.burman@ucl.ac.uk" class="auth_mail" title="E-mail the corresponding author} ; Isaac P. Santos^b ; ^{isaac.santos@ufes.br" class="auth_mail" title="E-mail the corresponding author}
• 关键词：Continuous dependence ; Advection&ndash ; diffusion equation ; Stabilized finite element method ; Error estimates
• 刊名：Journal of Computational and Applied Mathematics
• 出版年：2017
• 出版时间：1 January 2017
• 年：2017
• 卷：309
• 期：Complete
• 页码：267-286
• 全文大小：2963 K

文摘

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.