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

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.

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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.

Author Details

Ajmia Younes Orfi

Driss Yakoubi

  1. A posteriori error estimates of finite element method for the time-dependent Darcy problem in an axisymmetric domain

    Orfi, Ajmia Younes

    Yakoubi, Driss

    Computers & Mathematics with Applications, Vol. 77 (2019), Iss. 10 P.2833

    https://doi.org/10.1016/j.camwa.2019.01.016 [Citations: 1]