TY - JOUR T1 - A Priori Error Analysis of an Euler Implicit, Finite Element Approximation of the Unsteady Darcy Problem in an Axisymmetric Domain AU - Orfi , Ajmia Younes AU - Yakoubi , Driss JO - Advances in Applied Mathematics and Mechanics VL - 2 SP - 301 EP - 321 PY - 2018 DA - 2018/10 SN - 10 DO - http://doi.org/10.4208/aamm.OA-2016-0055 UR - https://global-sci.org/intro/article_detail/aamm/12213.html KW - Darcy's equations, axisymmetric domain, Fourier truncation, finite element discretization. AB -

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.