Volume 54, Number 3, May-June 2020
|Page(s)||1003 - 1023|
|Published online||28 April 2020|
A Γ-convergence result for fluid-filled fracture propagation
Zentrum Mathematik, M7, TU München, Boltzmannstr. 3, 85748
2 Angewandte Mathematik, WWU Münster, Einsteinstr. 62, 48149 Münster, Germany
* Corresponding author: firstname.lastname@example.org
Accepted: 3 March 2020
In this paper we provide a rigorous asymptotic analysis of a phase-field model used to simulate pressure-driven fracture propagation in poro-elastic media. More precisely, assuming a given pressure p ∈ W 1,∞ (Ω) we show that functionals of the form can be approximated in terms of Γ-convergence by a sequence of phase-field functionals, which are suitable for numerical simulations. The Γ-convergence result is complemented by a numerical example where the phase-field model is implemented using a Discontinuous Galerkin Discretization.
Mathematics Subject Classification: 49J45 / 74R10 / 65N30
Key words: Γ-convergence / phase-field approximation / pressure-driven crack propagation / discontinuous Galerkin method
© EDP Sciences, SMAI 2020
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