Guaranteed and computable error bounds for approximations constructed by an iterative decoupling of the Biot problem
Year of publication
2021
Authors
Kumar, Kundan; Kyas, Svetlana; Nordbotten, Jan Martin; Repin, Sergey
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.
Show moreOrganizations and authors
University of Jyväskylä
Repin Sergey
Publication type
Publication format
Article
Parent publication type
Journal
Article type
Original article
Audience
ScientificPeer-reviewed
Peer-ReviewedMINEDU's publication type classification code
A1 Journal article (refereed), original researchPublication channel information
Publisher
Volume
91
Pages
122-149
ISSN
Publication forum
Publication forum level
1
Open access
Open access in the publisher’s service
Yes
Open access of publication channel
Partially open publication channel
Self-archived
Yes
Other information
Fields of science
Mathematics
Keywords
[object Object],[object Object],[object Object],[object Object]
Publication country
United Kingdom
Internationality of the publisher
International
Language
English
International co-publication
Yes
Co-publication with a company
No
DOI
10.1016/j.camwa.2020.05.005
The publication is included in the Ministry of Education and Culture’s Publication data collection
Yes