We consider the time dependent Darcy problem in a three-dimensional axisymmetric domain and, by writing the Fourier expansion of its solution with respect to the angular variable, we observe that each Fourier coefficient satisfies a system of equations on the meridian domain. We propose a discretization of these equations in the case of general solution. This discretization relies on a backward Euler's scheme for the time variable and finite elements for the space variables. We prove a priori error estimates both for the time steps and the meshes.

}, issn = {2075-1354}, doi = {https://doi.org/10.4208/aamm.OA-2016-0055}, url = {http://global-sci.org/intro/article_detail/aamm/12213.html} }