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 employing the fixed-stress split scheme, which leads to a semi-discrete system solved iteratively. The error bounds are derived by combining a posteriori estimates for contractive mappings with those of the functional type for elliptic partial differential equations. The estimates are applicable for 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, which can be used in adaptive procedures.

中文翻译：

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由 Biot 问题的迭代解耦构造的近似值的有保证和可计算的误差界限

该论文涉及一类与由准静态线性 Biot 方程控制的多孔弹性介质相关的进化问题的保证后验误差估计。该系统采用固定应力拆分方案进行解耦，从而得到一个迭代求解的半离散系统。通过将收缩映射的后验估计与椭圆偏微分方程的函数类型的后验估计相结合，可以得出误差界限。这些估计适用于可容许函数空间中的任何近似值，并且独立于离散化方法。它们是完全可计算的，不包含网格相关常数，并提供能量范数中测量的误差的可靠全局估计。此外，他们为局部误差的分布提出了有效的误差指标，