Computational Geosciences

, Volume 22, Issue 4, pp 1021–1038 | Cite as

Robust iterative schemes for non-linear poromechanics

  • Manuel BorregalesEmail author
  • Florin A. Radu
  • Kundan Kumar
  • Jan M. Nordbotten
Original Paper


We consider a non-linear extension of Biot’s model for poromechanics, wherein both the fluid flow and mechanical deformation are allowed to be non-linear. Specifically, we study the case when the volumetric stress and the fluid density are non-linear functions satisfying certain assumptions. We perform an implicit discretization in time (backward Euler) and propose two iterative schemes for solving the non-linear problems appearing within each time step: a splitting algorithm extending the undrained split and fixed stress methods to non-linear problems, and a monolithic L-scheme. The convergence of both schemes are shown rigorously. Illustrative numerical examples are presented to confirm the applicability of the schemes and validate the theoretical results.


Biot’s model L-schemes MFEM Convergence analysis Fixed-stress method Coupled problems Poromechanics 


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Funding information

The research was supported by the University of Bergen in cooperation with the FME-SUCCESS center (grant 193825/S60) funded by the Research Council of Norway. The work has also been partly supported by the following: the NFR-DAADppp grant 255715, the NFR-Toppforsk project 250223, the NRC-CHI grant 255510, and the NRC-IMMENS grant 255426.


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© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of BergenBergenNorway
  2. 2.Department of Civil and Environmental EngineeringPrinceton UniversityPrincetonUSA

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