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Laboratoire Jacques-Louis Lions |  |
Journal articles
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.
https://hal.sorbonne-universite.fr/hal-03013610
Contributor : Gestionnaire Hal-Su <>
Submitted on : Thursday, November 19, 2020 - 9:16:10 AM
Last modification on : Tuesday, December 8, 2020 - 3:34:20 AM
Contributor : Gestionnaire Hal-Su <>
Submitted on : Thursday, November 19, 2020 - 9:16:10 AM
Last modification on : Tuesday, December 8, 2020 - 3:34:20 AM
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