A Posteriori Error Estimates for Biot System using Enriched Galerkin for Flow - Sorbonne Université
Journal Articles Computer Methods in Applied Mechanics and Engineering Year : 2020

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.
Fichier principal
Vignette du fichier
Girault et al. - 2020 - A posteriori error estimates for Biot system using.pdf (1.35 Mo) Télécharger le fichier
Origin Files produced by the author(s)

Dates and versions

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

Identifiers

Cite

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⟩
38 View
64 Download

Altmetric

Share

More