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Such nonlinear models are typically used to study biological structures like tissues, organs, cartilage and bones, which are known for a nonlinear dependence of their permeability\/hydraulic conductivity on solid dilatation. We formulate (extend to the present situation) one of the most popular splitting schemes, namely the fixed-stress split method for the iterative solution of the coupled problem. The method is proven to converge linearly for sufficiently small time steps under standard assumptions. The error contraction factor then is strictly less than one, independent of the Lam\u00e9 parameters, Biot and storage coefficients if the hydraulic conductivity is a strictly positive and Lipschitz-continuous function.<\/jats:p>","DOI":"10.1007\/s00366-024-02030-x","type":"journal-article","created":{"date-parts":[[2024,7,26]],"date-time":"2024-07-26T20:02:04Z","timestamp":1722024124000},"page":"4031-4042","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":3,"title":["A fixed-stress splitting method for nonlinear poroelasticity"],"prefix":"10.1007","volume":"41","author":[{"given":"Johannes","family":"Kraus","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Kundan","family":"Kumar","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Maria","family":"Lymbery","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Florin A.","family":"Radu","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2024,7,26]]},"reference":[{"key":"2030_CR1","doi-asserted-by":"crossref","unstructured":"Detournay E, Cheng AH-D (1993) Fundamentals of poroelasticity. 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