A Continuous Interior Penalty Method for Viscoelastic Flows

Abstract

In this paper we consider a finite element discretization of the Oldroyd-B model of viscoelastic flows. The method uses standard continuous polynomial finite element spaces for velocities, pressures and stresses. Inf-sup stability and stability for convection-dominated flows are obtained by adding a term penalizing the jump of the solution gradient over element faces. To increase robustness when the Deborah number is high we add a non-linear artificial viscosity of shock-capturing type. The method is analyzed on a linear model problem, optimal a priori error estimates are proven that are independent of the solvent viscosity ηs. Finally we demonstrate the performance of the method on some known benchmark cases. AMS subject classifications. 65N12, 65N30, 76A10, 76M10

DOI: 10.1137/060677033

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Cite this paper

@article{Bonito2008ACI, title={A Continuous Interior Penalty Method for Viscoelastic Flows}, author={Andrea Bonito and Erik Burman}, journal={SIAM J. Scientific Computing}, year={2008}, volume={30}, pages={1156-1177} }