Abstract
In this paper, we study the time-dependent Darcy and Stokes equations, that model laminar fluid flow over a porous medium, in two- or three-dimensional connected open domains which are coupled via appropriate matching conditions on the interface. The problem is discretized by the backward Euler scheme in time and finite elements in space. We prove a priori error estimates as a function of the time steps and for the meshes.
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Bernardi, C., Orfi, A.Y. A priori error analysis of the fully discretized time-dependent coupled Darcy and Stokes equations. SeMA 73, 97–119 (2016). https://doi.org/10.1007/s40324-015-0058-5
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DOI: https://doi.org/10.1007/s40324-015-0058-5