Volume 10, Issue 2
A Priori Error Analysis of an Euler Implicit, Finite Element Approximation of the Unsteady Darcy Problem in an Axisymmetric Domain

Ajmia Younes Orfi and Driss Yakoubi

10.4208/aamm.OA-2016-0055

Adv. Appl. Math. Mech., 10 (2018), pp. 301-321

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  • Abstract

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.

  • History

Published online: 2018-10

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