A Continuous Interior Penalty Method for Viscoelastic Flows
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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 nonlinear artificial viscosity of shock-capturing type. The method is analyzed on a linear model problem, and optimal a priori errorestimates are proven that are independent of the solvent viscosity Finally we demonstrate the performance of the method on some known benchmark cases. 2008 Society for Industrial and Applied Mathematics.
SIAM Journal on Scientific Computing
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Bonito, Andrea||Burman, Erik