A UNIFIED STABILIZED FINITE VOLUME METHOD FOR STOKES AND DARCY EQUATIONS
J. Korean Math. Soc.
Published online 2019 Feb 12
Akram Boukabache and Nasserdine Kechkar
Laboratory of Pure and Applied Mathematics, University of Jijel, Jijel, Algeria, Department of Mathematics. 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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