Abstract
We consider the discretization of the stationary Navier–Stokes/Darcy system in a two-dimensional domain by the non-conforming finite volume element method. We use the standard formulation of the Navier–Stokes/Darcy system in the primitive variables and take as approximation space the non-conforming \(P_{1}\) elements for velocity and piezometric head and piecewise constant elements for the hydrostatic pressure. We prove that the unique solution of the non-conforming finite volume element method converges to the true solution with optimal order for velocity and piezometric head in discrete \(H^{1}\) norm and for pressure in discrete \(L^{2}\) norm, respectively. Finally, some numerical experiments are presented to validate our theoretical results.
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The work was supported by the National Natural Science Fund of China (11371289).
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Communicated by Domingo Alberto Tarzia.
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Wu, Y., Mei, L. A non-conforming finite volume element method for the two-dimensional Navier–Stokes/Darcy system . Comp. Appl. Math. 37, 457–474 (2018). https://doi.org/10.1007/s40314-016-0355-3
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DOI: https://doi.org/10.1007/s40314-016-0355-3