Guaranteed and computable error bounds for approximations constructed by an iterative decoupling of the Biot problem. (1st June 2021)

• Record Type: Journal Article
• Authors: Kumar, Kundan; Kyas, Svetlana; Nordbotten, Jan Martin; Repin, Sergey
• Is Part Of: Computers & mathematics with applications. Volume 91(2021)
• Page Start: 122
• Page End: 149
• Publication Date: 2021-06-01
• Subjects: Biot problem -- Fixed-stress split iterative scheme -- a posteriori error estimates -- Contraction mappings; Electronic data processing -- Periodicals; Mathematics -- Data processing -- Periodicals; 510.28541
• DOI: 10.1016/j.camwa.2020.05.005
• Languages: English
• ISSNs: 0898-1221

Abstract

Abstract: 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.