In this work we consider the coupled problem of Darcy flow in a fracture and the surrounding porous medium. The fracture is represented as a (d - 1)-dimensional interface, and it is nonmatching with the computational grid thanks to a suitable extended finite element method (XFEM) enrichment of the mixed finite element spaces. In the existing literature well posedness has been proven for the discrete problem in the hypothesis of a given solution in the fracture. This work provides theoretical results on the stability and convergence of the discrete, fully coupled problem, yielding sharp conditions on the fracture geometry and on the computational grid to ensure that the inf-sup condition is satisfied by the enriched spaces, as confirmed by numerical experiments.

Well posedness of fully coupled fracture/bulk darcy flow with XFEM

DEL PRA, MARCO;FUMAGALLI, ALESSIO;SCOTTI, ANNA
2017-01-01

Abstract

In this work we consider the coupled problem of Darcy flow in a fracture and the surrounding porous medium. The fracture is represented as a (d - 1)-dimensional interface, and it is nonmatching with the computational grid thanks to a suitable extended finite element method (XFEM) enrichment of the mixed finite element spaces. In the existing literature well posedness has been proven for the discrete problem in the hypothesis of a given solution in the fracture. This work provides theoretical results on the stability and convergence of the discrete, fully coupled problem, yielding sharp conditions on the fracture geometry and on the computational grid to ensure that the inf-sup condition is satisfied by the enriched spaces, as confirmed by numerical experiments.
2017
Extended finite element; flows in fractured porous media; Stability of mixed finite element; Numerical Analysis
File in questo prodotto:
File Dimensione Formato  
Well Posedness_SIAM Jour.Num.Anal.

Accesso riservato

: Publisher’s version
Dimensione 1.13 MB
Formato Unknown
1.13 MB Unknown   Visualizza/Apri
11311-1029496 Scotti.pdf

accesso aperto

: Pre-Print (o Pre-Refereeing)
Dimensione 1.01 MB
Formato Adobe PDF
1.01 MB Adobe PDF Visualizza/Apri

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11311/1029496
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 26
  • ???jsp.display-item.citation.isi??? 21
social impact