A stabilized Lagrange multiplier finite-element method for flow in porous media with fractures - Archive ouverte HAL Access content directly
Journal Articles GEM - International Journal on Geomathematics Year : 2019

A stabilized Lagrange multiplier finite-element method for flow in porous media with fractures

Abstract

In this work we introduce a stabilized, numerical method for a multi-dimensional, discrete-fracture model (DFM) for single-phase Darcy flow in fractured porous media. In the model, introduced in an earlier work, flow in the (n − 1)-dimensional fracture domain is coupled with that in the n-dimensional bulk or matrix domain by the use of Lagrange multipliers. Thus the model permits a finite element discretization in which the meshes in the fracture and matrix domains are independent so that irregular meshing and in particular the generation of small elements can be avoided. In this paper we introduce in the numerical formulation, which is a saddle-point problem based on a primal, variational formulation for flow in the matrix domain and in the fracture system, a consistent stabilizing term which penalizes discontinuities in the Lagrange multipliers. For this penalized scheme we show stability and prove convergence. With numerical experiments we analyze the performance of the method for various choices of the penalization parameter and compare with other numerical DFM's.
Fichier principal
Vignette du fichier
articleHAL.pdf (1.09 Mo) Télécharger le fichier
Origin : Files produced by the author(s)
Loading...

Dates and versions

hal-01761591 , version 1 (09-04-2018)
hal-01761591 , version 2 (18-11-2018)
hal-01761591 , version 3 (29-12-2018)

Identifiers

Cite

Markus Köppel, Vincent Martin, Jean E. Roberts. A stabilized Lagrange multiplier finite-element method for flow in porous media with fractures. GEM - International Journal on Geomathematics, In press, ⟨10.1007/s13137-019-0117-7⟩. ⟨hal-01761591v3⟩
649 View
251 Download

Altmetric

Share

Gmail Facebook X LinkedIn More