2023
DOI: 10.1090/mcom/3809
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An iterative decoupled algorithm with unconditional stability for Biot model

Abstract: This paper is concerned with numerical algorithms for Biot model. By introducing an intermediate variable, the classical 2-field Biot model is written into a 3-field formulation. Based on such a 3-field formulation, we propose a coupled algorithm, some time-extrapolation based decoupled algorithms, and an iterative decoupled algorithm. Our focus is the analysis of the iterative decoupled algorithm. It is shown that the convergence of the iterative decoupled algorithm requires no extra assumptions on physical p… Show more

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Cited by 2 publications
(2 citation statements)
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“…Detailed numerical experiments are carried out to verify the predictions of error estimates. In future work, we plan to develop some decoupled algorithms [11,14] and the corresponding analysis based on the theory studied in this work.…”
Section: Discussionmentioning
confidence: 99%
See 1 more Smart Citation
“…Detailed numerical experiments are carried out to verify the predictions of error estimates. In future work, we plan to develop some decoupled algorithms [11,14] and the corresponding analysis based on the theory studied in this work.…”
Section: Discussionmentioning
confidence: 99%
“…Instead of providing cumulative H1$$ {H}^1 $$ error estimates or rough H1$$ {H}^1 $$ error estimates for pressure [7,10], our research presents rigorous H1$$ {H}^1 $$ error estimates of pressure at the final time, drawing inspiration from [16,23]. Furthermore, the unconditional convergence of Method 2 suggests that such a second order method can also be applied to iterative schemes for Biot's model [3,4,11], significantly enhancing computational efficiency. We comment here that the theoretical framework in this work can be extended to provide a novel perspective for analyzing decoupled schemes [14,17] that offer high efficiency and superconvergence.…”
Section: Introductionmentioning
confidence: 99%