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A Posteriori Error Estimates for Biot System using Enriched Galerkin for Flow

Abstract : We analyze the Biot system solved with a fixed-stress split, Enriched Galerkin (EG) discretiza-tion for the flow equation, and Galerkin for the mechanics equation. Residual-based a posteriori error estimates are established with both lower and upper bounds. These theoretical results are confirmed by numerical experiments performed with Mandel's problem. The efficiency of these a posteriori error estimators to guide dynamic mesh refinement is demonstrated with a prototype unconventional reservoir model containing a fracture network. We further propose a novel stopping criterion for the fixed-stress iterations using the error indicators to balance the fixed-stress split error with the discretization errors. The new stopping criterion does not require hyperparameter tuning and demonstrates efficiency and accuracy in numerical experiments.
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Submitted on : Thursday, November 19, 2020 - 9:16:10 AM
Last modification on : Tuesday, December 8, 2020 - 3:34:20 AM


Girault et al. - 2020 - A post...
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Vivette Girault, Xueying Lu, Mary Wheeler. A Posteriori Error Estimates for Biot System using Enriched Galerkin for Flow. Computer Methods in Applied Mechanics and Engineering, Elsevier, 2020, 369, pp.113185. ⟨10.1016/j.cma.2020.113185⟩. ⟨hal-03013610⟩



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