Robust a posteriori error estimation for mixed finite element approximation of linear poroelasticity
Robust a posteriori error estimation for mixed finite element approximation of linear poroelasticity
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DOI：
10.1093/imanum/draa058
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发表时间：
2020-07
影响因子：
2.1
通讯作者：
Arbaz Khan;D. Silvester
中科院分区：
文献类型：
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作者：
Arbaz Khan;D. Silvester
这部作品是为了纪念约翰·W。Barrett在1981年的MAFEUNK会议上向酒吧的通讯作者介绍了inf-sup稳定性的概念。本文分析了毕奥固结模型无锁定混合有限元逼近的后验误差估计。三个估计描述。其中最简单的是传统的基于残差的估计器。我们建立的估计和真实误差的界限，并表明，这些是独立的物理参数。其他两个估计需要解决当地的问题。这些局部问题估计也被证明是可靠的，有效的和强大的。数值结果验证了理论估计，并说明在指导自适应解决方案的算法估计的有效性。用于计算实验的IFISS和T-IFISS软件包可在线获得。
This work is dedicated to the memory of John W. Barrett, who introduced the concept of inf–sup stability to the corresponding author in the bar at the MAFELAP conference in 1981. We analyze a posteriori error estimators for locking-free mixed finite element approximation of Biot’s consolidation model. Three estimators are described. The simplest of these is a conventional residual-based estimator. We establish bounds relating the estimated and true errors, and show that these are independent of the physical parameters. The other two estimators require the solution of local problems. These local problem estimators are also shown to be reliable, efficient and robust. Numerical results are presented that validate the theoretical estimates, and illustrate the effectiveness of the estimators in guiding adaptive solution algorithms. The IFISS and T-IFISS software packages used for the computational experiments are available online.