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Error analysis of finite element and finite volume methods for some viscoelastic fluids

Mária Lukáčová-Medvid’ová, Hana Mizerová, Bangwei She and Jan Stebel

Abstract

We present the error analysis of a particular Oldroyd-B type model with the limiting Weissenberg number going to infinity. Assuming a suitable regularity of the exact solution we study the error estimates of a standard finite element method and of a combined finite element/finite volume method. Our theoretical result shows first order convergence of the finite element method and the error of the order đť“ž(h3/4) for the finite element/finite volume method. These error estimates are compared and confirmed by the numerical experiments.

Acknowledgment

B.S. and H.M. would like to thank Profs. Tabata and Notsu (Waseda University, Tokyo) for fruitful discussions on the topic.

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Received: 2014-8-8
Revised: 2015-2-1
Accepted: 2015-2-3
Published Online: 2016-6-8
Published in Print: 2016-6-1

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