Keywords
Darcy's equations
numerical analysis
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Abstract
This paper is devoted to the approximation of a
nonstandard Darcy problem, which modelizes the flow in porous media, by
spectral methods: the pressure is assigned on a part of the boundary.
We propose two variational formulations, as well as three spectral
discretizations. The second discretization improves the approximation of the
divergence-free condition, but the error estimate on the pressure is not
optimal, while the third one leads to optimal error estimate with a
divergence-free discrete solution, which is important for some
applications. Next, their numerical analysis is performed in detail
and we present some numerical experiments which confirm the interest
of the third discretization.
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