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 - <p style="text-align: justify;">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&#39;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.</p>