Abstract
We discretize in space the equations obtained at each time step when discretizing in time a Navier-Stokes system modelling the two-dimensional flow in a horizontal pipe of two immiscible fluids with comparable densities, but very different viscosities. At each time step the system reduces to a generalized Stokes problem with nonstandard conditions at the boundary and at the interface between the two fluids. We discretize this system with the “mini-element” and establish error estimates. © 2005 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2005
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