A unified stabilized finite volume method for Stokes and Darcy equations
J. Korean Math. Soc. 2019 Vol. 56, No. 4, 1083-1112
Published online July 1, 2019
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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