A Priori Error Analysis of an Euler Implicit, Finite Element Approximation of the Unsteady Darcy Problem in an Axisymmetric Domain
Year: 2018
Author: Ajmia Younes Orfi, Driss Yakoubi
Advances in Applied Mathematics and Mechanics, Vol. 10 (2018), Iss. 2 : pp. 301–321
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.
You do not have full access to this article.
Already a Subscriber? Sign in as an individual or via your institution
Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/aamm.OA-2016-0055
Advances in Applied Mathematics and Mechanics, Vol. 10 (2018), Iss. 2 : pp. 301–321
Published online: 2018-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 21
Keywords: Darcy's equations axisymmetric domain Fourier truncation finite element discretization.