论文标题
BIOT合并模型的两个完全离散耦合方案的先验错误估计
A priori error estimates of two fully discrete coupled schemes for Biot's consolidation model
论文作者
论文摘要
本文集中于基于Oyarzua等人引入的三场公式的Biot合并模型的两个完全离散耦合方案的先验误差估计。 （《暹罗杂志》，《数值分析》，2016年）。空间离散是基于泰勒 - 霍德有限元素，结合了三个主要变量的拉格朗日元素。对于时间离散，我们考虑两种方法。一个使用后向欧拉方法，另一个使用后向欧拉和曲柄 - 尼科尔森方法的组合。先验错误估计表明，这两个方案是无条件收敛的，并具有最佳的误差顺序。提出了详细的数值实验以验证理论分析。
This paper concentrates on a priori error estimates of two fully discrete coupled schemes for Biot's consolidation model based on the three-field formulation introduced by Oyarzua et al. (SIAM Journal on Numerical Analysis, 2016). The spatial discretizations are based on the Taylor-Hood finite elements combined with Lagrange elements for the three primary variables. For time discretization, we consider two methods. One uses the backward Euler method, and the other applies a combination of the backward Euler and Crank-Nicolson methods. A priori error estimates show that the two schemes are unconditionally convergent with optimal error orders. Detailed numerical experiments are presented to validate the theoretical analysis.
