A stabilized three fields formulation for Discrete Fracture Networks

TL;DR

This paper introduces a stabilized hybridized domain decomposition method for discrete fracture networks that allows independent discretization of fractures, ensuring stability and accuracy without compatibility constraints.

Contribution

It presents a novel stabilized formulation that removes the need for inf-sup conditions, enabling independent discretization and providing proven stability and error estimates.

Findings

Optimal stability and error estimates are established.

Numerical tests confirm the theoretical results.

The method allows independent discretization of fractures.

Abstract

We propose a hybridized domain decomposition formulation of the discrete fracture network model, allowing for independent discretization of the individual fractures. A natural norm stabilization, obtained by penalizing the residual measured in the norm for the space where it naturally lives, is added to the local problem in the individual fracture so that no compatibility condition of inf-sup type is required between the Lagrange multiplier and the primal unknown, which can then be discretized independently of each other. Optimal stability and error estimates are proven, which are confirmed by numerical tests.