The paper is concerned with guaranteed a posteriori error estimates for a class of evolutionary problems related to poroelastic media governed by the quasi-static linear Biot equations. The system is decoupled by employing the fixed-stress split scheme, which leads to an iteratively solved semi-discrete system. The error bounds are derived by combining a posteriori estimates for contractive mappings with functional type error control for elliptic partial differential equations. The estimates are applicable to any approximation in the admissible functional space and are independent of the discretization method. They are fully computable, do not contain mesh-dependent constants, and provide reliable global estimates of the error measured in the energy norm. Moreover, they suggest efficient error indicators for the distribution of local errors and can be used in adaptive procedures.

本文关注的是由准静态线性Biot方程控制的与多孔弹性介质有关的一类演化问题的后验误差估计。该系统通过采用固定应力拆分方案进行解耦，从而产生了迭代求解的半离散系统。通过将用于压缩映射的后验估计与用于椭圆型偏微分方程的函数类型误差控制相结合，得出误差范围。估计值适用于允许的功能空间中的任何近似值，并且与离散化方法无关。它们是完全可计算的，不包含与网格相关的常数，并且可以对在能量范式中测量的误差提供可靠的全局估计。此外，