论文标题
用于辅助合并的生物模型的新的多物理有限元方法
A new multiphysics finite element method for a Biot model with secondary consolidation
论文作者
论文摘要
在本文中,我们提出了一种新的多物理有限元方法,用于在土壤动力学中具有二次巩固的生物模型。为了更好地描述原始模型中的变形和扩散过程,我们通过一种新的多物理学方法重新重新制定了Biot模型,该方法将流体固定的耦合问题转化为流体耦合问题 - 一个广义的Stokes问题和扩散问题。然后,我们给出弱解决方案的能量定律和先前的误差估计。我们设计了一个完全离散的时间步骤方案,用于使用$ P_2-P_1-P_1 $元素对的混合有限元方法,以近似时间变量的空间变量和向后的Euler方法,我们证明了离散的能量法律和最佳收敛误差顺序估计。另外,我们展示了一些数值示例,以验证理论结果。最后,我们得出一个结论来总结本文的主要结果。
In this paper, we propose a new multiphysics finite element method for a Biot model with secondary consolidation in soil dynamics. To better describe the processes of deformation and diffusion underlying in the original model, we reformulate Biot model by a new multiphysics approach, which transforms the fluid-solid coupled problem to a fluid coupled problem--a generalized Stokes problem and a diffusion problem. Then, we give the energy law and prior error estimate of the weak solution. And we design a fully discrete time-stepping scheme to use mixed finite element method for $P_2-P_1-P_1$ element pairs to approximate the space variables and backward Euler method for the time variable, and we prove the discrete energy laws and the optimal convergence order error estimates. Also, we show some numerical examples to verify the theoretical results. Finally, we draw a conclusion to summarize the main results of this paper.