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- W2086098462 abstract "We analyze a finite element discretization of the Brinkman equation for modeling non-Darcian fluid flow by allowing the Brinkman viscosity $tilde{nu}rightarrowinfty$ and permeability $Krightarrow0$ in solid obstacles, and $Krightarrowinfty$ in the fluid domain. In this context, the Brinkman parameters are generally highly discontinuous. Furthermore, we consider nonhomogeneous Dirichlet boundary conditions $mathbf{u}|_{partialOmega}=phineq0$ and nonsolenoidal velocity $nablacdotmathbf{u}=gneq0$ (to model sources/sinks). Coupling between these two conditions makes even existence of solutions subtle. We establish well-posedness of the continuous and discrete problem, a priori stability estimates, and convergence as $tilde{nu}rightarrowinfty$ and $Krightarrow0$ in solid obstacles, as $Krightarrowinfty$ in the fluid region, and as the mesh width $hrightarrow0$. For nonsolenoidal Brinkman flows, we include a small data condition on $phi$ and g to ensure existence of solutions (a similar conclusion is attainable for existence of solutions to the steady Navier–Stokes equations with nonhomogeneous data)." @default.
- W2086098462 created "2016-06-24" @default.
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- W2086098462 date "2011-01-01" @default.
- W2086098462 modified "2023-09-27" @default.
- W2086098462 title "Finite Element Approximation of Nonsolenoidal, Viscous Flows around Porous and Solid Obstacles" @default.
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- W2086098462 doi "https://doi.org/10.1137/090765341" @default.
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