A Study on the Galerkin Least-Squares Method for the Oldroyd-B Model-Reference-Cited by-同舟云学术

A Study on the Galerkin Least-Squares Method for the Oldroyd-B Model

Published:2017-07-06 Issue:2 Volume:18 Page:181-198
ISSN:1609-9389
Container-title:Computational Methods in Applied Mathematics
language:en
Short-container-title:

Author:

Chen Tsu-Fen¹,Lee Hyesuk²,Liu Chia-Chen³

Affiliation:

1. Department of Mathematics , National Chung Cheng University , Chia-Yi 621 , Taiwan

2. Department of Mathematical Sciences , Clemson University , Clemson , SC 29634-0975 , USA

3. National Bei-Gang Senior High School , Yunlin 651 , Taiwan

Abstract

Abstract We consider a reduced Galerkin least-squares finite element method for the Oldroyd-B model of viscoelastic fluid flows. Model problems considered are the flow past a planar channel and a 4-to-1 contraction problems. An a priori error estimate for the reduced Galerkin least-squares method is derived and numerical results supporting the estimate are presented.

Funder

National Science Foundation

Publisher

Walter de Gruyter GmbH

Subject

Applied Mathematics,Computational Mathematics,Numerical Analysis

Reference27 articles.

1. F. P. T. Baaijens, Application of low-order discontinuous Galerkin methods to the analysis of viscoelastic flows, J. Non-Newtonian Fluid Mech. 52 (1994), 37–57.

2. F. P. T. Baaijens, Mixed finite element methods for viscoelastic flow analysis: A review, J. Non-Newtonian Fluid Mech. 79 (1998), 361–385.

3. J. Baranger and D. Sandri, Finite element approximation of viscoelastic fluid flow: Existence of approximate solutions and error bounds. I: Discontinuous constraints, Numer. Math. 63 (1992), no. 1, 13–27.

4. M. Behr, D. Arora and M. Pasquali, Stabilized finite element methods of GLS type for Maxwell-B and Oldroyd-B viscoelastic fluids, Proceedings of the European Congress on Computational Methods in Applied Sciences and Engineering (ECCOMAS 2004), http://www.mit.jyu.fi/eccomas2004/proceedings/pdf/728.pdf.

5. R. B. Bird, R. C. Armstrong and O. Hassager, Dynamics of Polymeric Liquids. Vol. 1: Fluid Mechanics, John Wiley and Sons, New York, 1987.