A Posteriori Error Estimates for Biot System using Enriched Galerkin for Flow - Sorbonne Université
Article Dans Une Revue Computer Methods in Applied Mechanics and Engineering Année : 2020

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

Résumé

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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Dates et versions

hal-03013610 , version 1 (19-11-2020)

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