Journal of the
Korean Mathematical Society
JKMS

ISSN(Print) 0304-9914 ISSN(Online) 2234-3008

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J. Korean Math. Soc. 2019; 56(4): 1083-1112

Online first article February 12, 2019      Printed July 1, 2019

https://doi.org/10.4134/JKMS.j180641

Copyright © The Korean Mathematical Society.

A unified stabilized finite volume method for Stokes and Darcy equations

Akram Boukabache, Nasserdine Kechkar

University Mohamed Seddik Benyahia; University Freres Mentouri

Abstract

In this paper, we present and analyze a cell-centered collocated finite volume scheme for incompressible flows to compute solutions simultaneous to Stokes and Darcy equations by applying a pressure jump stabilization term to avoid locking. We prove that the new stabilized FV formulation satisfies a discrete inf-sup condition and error estimates for both problems. Finally, we present some numerical examples confirming this analysis.

Keywords: finite volumes, collocated discretizations, Stokes equation, Darcy equation, stabilized methods

MSC numbers: 65N08, 65N12, 65N15, 65N30, 76D07

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