A1 Journal article (refereed)
Guaranteed and computable error bounds for approximations constructed by an iterative decoupling of the Biot problem (2021)

Kumar, K., Kyas, S., Nordbotten, J. M., & Repin, S. (2021). Guaranteed and computable error bounds for approximations constructed by an iterative decoupling of the Biot problem. Computers and Mathematics with Applications , 91, 122-149. https://doi.org/10.1016/j.camwa.2020.05.005

JYU authors or editors

Publication details

All authors or editors: Kumar, Kundan; Kyas, Svetlana; Nordbotten, Jan Martin; Repin, Sergey

Journal or series: Computers and Mathematics with Applications

ISSN: 0898-1221

eISSN: 1873-7668

Publication year: 2021

Volume: 91

Pages range: 122-149

Publisher: Elsevier

Publication country: United Kingdom

Publication language: English

DOI: https://doi.org/10.1016/j.camwa.2020.05.005

Publication open access: Openly available

Publication channel open access: Partially open access channel

Publication is parallel published (JYX): https://jyx.jyu.fi/handle/123456789/70911

Publication is parallel published: https://arxiv.org/abs/1808.08036


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.

Keywords: partial differential equations; numerical analysis; approximation; error analysis

Free keywords: Biot problem; fixed-stress split iterative scheme; a posteriori error estimates; contraction mappings

Contributing organizations

Ministry reporting: Yes

Reporting Year: 2021

Preliminary JUFO rating: 1

Last updated on 2022-17-06 at 11:22