Bulletin of the
Korean Mathematical Society
BKMS

ISSN(Print) 1015-8634 ISSN(Online) 2234-3016

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Bull. Korean Math. Soc. 2014; 51(1): 267-285

Printed January 1, 2014

https://doi.org/10.4134/BKMS.2014.51.1.267

Copyright © The Korean Mathematical Society.

An upstream pseudostress-velocity mixed formulation for the Oseen equations

Eun-Jae Park and Boyoon Seo

Yonsei University, Yonsei University

Abstract

An upstream scheme based on the pseudostress-velocity mixed formulation is studied to solve convection-dominated Oseen equations. Lagrange multipliers are introduced to treat the trace-free constraint and the lowest order Raviart-Thomas finite element space on rectangular mesh is used. Error analysis for several quantities of interest is given. Particularly, first-order convergence in $L^2$ norm for the velocity is proved. Finally, numerical experiments for various cases are presented to show the efficiency of this method.

Keywords: pseudostress-velocity formulation, upstream scheme, mixed finite element, Oseen equations

MSC numbers: Primary 58B34, 58J42, 81T75

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