Equal Lower-order Finite Elements of Least-squares Type in Biot Poroelasticity Modeling

IF 0.6 4区 数学 Q3 MATHEMATICS
Hsueh-Chen Lee, Hyesuk Lee
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引用次数: 0

Abstract

We investigate the behavior of the approximate solution of Biot's consolidation model using a weighted least-squares (WLS) finite element method. The model describes the fluid flow in a deformable porous medium, with variables for fluid pressure, velocity, and displacement. The WLS functional is defined based on the stress-displacement formulation, with the symmetry condition of the stress and the weight that depends on the time step size for the temporal discretization of the model. An a priori error estimate for the first-order linearized least squares (LS) system is analyzed, and its validity is confirmed through numerical results. By using continuous piecewise linear finite element spaces for all variables and adjusting the weight appropriately, we obtain optimal error convergence rates for all variables. Additionally, we present two numerical examples to demonstrate the implementation of the WLS method for benchmark problems.
生物孔隙弹性模型中最小二乘型等低阶有限元
本文采用加权最小二乘(WLS)有限元法研究了Biot固结模型近似解的行为。该模型描述了流体在可变形多孔介质中的流动,变量包括流体压力、速度和位移。WLS泛函是基于应力-位移公式定义的,其应力和权值的对称条件取决于模型时间离散化的时间步长。分析了一阶线性化最小二乘(LS)系统的先验误差估计方法,并通过数值结果验证了其有效性。通过对所有变量使用连续分段线性有限元空间,并适当调整权值,得到了所有变量的最优误差收敛率。此外,我们给出了两个数值示例来演示WLS方法在基准问题中的实现。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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来源期刊
CiteScore
1.10
自引率
0.00%
发文量
35
审稿时长
3 months
期刊介绍: The Taiwanese Journal of Mathematics, published by the Mathematical Society of the Republic of China (Taiwan), is a continuation of the former Chinese Journal of Mathematics (1973-1996). It aims to publish original research papers and survey articles in all areas of mathematics. It will also occasionally publish proceedings of conferences co-organized by the Society. The purpose is to reflect the progress of the mathematical research in Taiwan and, by providing an international forum, to stimulate its further developments. The journal appears bimonthly each year beginning from 2008.
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