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

Keywords

Advanced Numerical Methods for Scientific Computing
Code:
25/2015
Title:
Well posedness of fully coupled fracture/bulk Darcy flow with XFEM
Date:
Monday 25th May 2015
Author(s):
Del Pra, M.; Fumagalli, A.; Scotti, A.
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Abstract:
In this work we consider the coupled problem of Darcy’s flow in a fracture and the surrounding porous medium. The fracture is represented as a (d ? 1)-dimensional interface and it is non-matching with the computational grid thanks to a suitable 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 given solution in the fracture. This works 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 conditions is satisfied by the enriched spaces, as confirmed by numerical experiments.
This report, or a modified version of it, has been also submitted to, or published on
SIAM Journal on Numerical Analysis (SINUM)