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 & Driss Yakoubi

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

Published online: 2018-10

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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.

  • Keywords

Darcy's equations, axisymmetric domain, Fourier truncation, finite element discretization.

  • AMS Subject Headings

65M60, 65M60, 65M15, 76D07, 76M10, 76S05

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{AAMM-10-301, author = {Ajmia Younes Orfi , and Yakoubi , Driss}, title = {A Priori Error Analysis of an Euler Implicit, Finite Element Approximation of the Unsteady Darcy Problem in an Axisymmetric Domain}, journal = {Advances in Applied Mathematics and Mechanics}, year = {2018}, volume = {10}, number = {2}, pages = {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.

}, issn = {2075-1354}, doi = {https://doi.org/10.4208/aamm.OA-2016-0055}, url = {http://global-sci.org/intro/article_detail/aamm/12213.html} }
TY - JOUR T1 - A Priori Error Analysis of an Euler Implicit, Finite Element Approximation of the Unsteady Darcy Problem in an Axisymmetric Domain AU - Ajmia Younes Orfi , 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.

Ajmia Younes Orfi & Driss Yakoubi. (2020). A Priori Error Analysis of an Euler Implicit, Finite Element Approximation of the Unsteady Darcy Problem in an Axisymmetric Domain. Advances in Applied Mathematics and Mechanics. 10 (2). 301-321. doi:10.4208/aamm.OA-2016-0055
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