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Asymptotic analysis and error estimates of mixed finite element method for Brinkman model. (English) Zbl 1383.76345

Summary: In this paper, we study a one-continuum model approach, so-called Brinkman model, to deal with Navier-Stokes-Darcy coupling problem in which the fluid flow exist in both the open channels and porous media. A parameter re-scaling technique is used to reformulate the traditional Brinkman model to a new one in order to investigate its asymptotic accuracy to Stokes and Darcy’s equations, respectively. We attain the convergence theorem in quantitative measure with respect to the dimensionless permeability parameter. We also analyze the error estimates of mixed finite element method for Brinkman model and Forchheimer model, and obtain the optimal convergence rates for both velocity and pressure. Numerical experiments validate the convergence results with respect to the permeability parameter and mesh size for both Brinkman model and Forchheimer model.

MSC:

76M10 Finite element methods applied to problems in fluid mechanics
65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
76S05 Flows in porous media; filtration; seepage
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