We consider a model coupling the Darcy equations in a porous medium with the Navier-Stokes equations in the cracks, for which the coupling is provided by the pressure's continuity on the interface. We discretize the coupled problem by the spectral element method combined with a nonoverlapping domain decomposition method. We prove the existence of solution for the discrete problem and establish an error estimation. We conclude with some numerical tests confirming the results of our analysis.
We consider the Laplace equation posed in a three-dimensional axisymmetric domain. We reduce the original problem by a Fourier expansion in the angular variable to a countable family of two-dimensional problems. We decompose the meridian domain, assumed polygonal, in a finite number of rectangles and we discretize by a spectral method. Then we describe the main features of the mortar method and use the algorithm Strang Fix to improve the accuracy of our discretization.
We consider the Laplace equation posed in a three-dimensional axisymmetric domain. We
reduce the original problem by a Fourier expansion in the angular variable to a countable
family of two-dimensional problems. We decompose the meridian domain, assumed polygonal,
in a finite number of rectangles and we discretize by a spectral method. Then we describe
the main features of the mortar method and use the algorithm Strang Fix to improve the
accuracy...
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