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.

翻译：本文件侧重于根据Oyarzua等人提出的三野配方(SIAM《数值分析杂志》,2016年)对Biot合并模型的两个完全分离的组合计划所作的先验误差估计,空间离散基于泰勒-胡德的有限元素,加上三个主要变量的拉格兰元素。关于时间分解,我们考虑两种方法。一种采用后向尤拉法,另一种采用落后的欧勒法和克兰克-尼科尔森法相结合的方法。先验误差估计表明,两种计划无条件与最佳误差顺序一致。为了验证理论分析,提供了详细的数字实验。