Abstract
In this paper we present the numerical analysis of a finite element method for a linearized viscoelastic flow problem. In particular, we analyze a linearization of the logarithmic reformulation of the problem, which in particular should be able to produce results for Weissenberg numbers higher than the standard one. In order to be able to use the same interpolation for all the unknowns (velocity, pressure and logarithm of the conformation tensor), we employ a stabilized finite element formulation based on the Variational Multi-Scale concept. The study of the linearized problem already serves to show why the logarithmic reformulation performs better than the standard one for high Weissenberg numbers; this is reflected in the stability and error estimates that we provide in this paper.
Funder
Institució Catalana de Recerca i Estudis Avançats
Subject
Applied Mathematics,Modeling and Simulation,Numerical Analysis,Analysis,Computational Mathematics
Cited by
1 articles.
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