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

作者：Orfi Ajmia Younes; Yakoubi Driss^*

来源：Advances in Applied Mathematics and Mechanics, 2018, 10(2): 301-321.

DOI：10.4208/aamm.OA-2016-0055

• Darcy's equations
• axisymmetric domain
• Fourier truncation
• finite element discretization

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.

• 出版日期2018-4