A posteriori error estimates of finite element method for the time-dependent Darcy problem in an axisymmetric domain
A posteriori error estimates of finite element method for the time-dependent Darcy problem in an axisymmetric domain
复制标题
轴对称域含时达西问题的有限元后验误差估计
DOI：
10.1016/j.camwa.2019.01.016
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发表时间：
2019
期刊：
影响因子：
--
通讯作者：
D. Yakoubi
中科院分区：
文献类型：
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作者：
Ajmia Younes Orfi;D. Yakoubi
我们考虑三维轴对称域中的时间相关达西问题，并通过写出其解相对于角度变量的傅里叶展开，我们观察到每个傅里叶系数满足子午域上的方程组。我们建议在通解的情况下对这些方程进行离散化。这种离散化依赖于时间变量的后向欧拉方案和空间变量的有限元。我们证明了后验误差估计，可以为时间步长和网格提供有效的自适应策略。给出了具有已知解的示例的计算，其支持后验误差估计。
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 posteriori error estimates that allow for an efficient adaptivity strategy both for the time steps and the meshes. Computations for an example with a known solution are presented which support the a posteriori error estimate.