Asymptotic analysis for the coupling between subdomains in Discrete Fracture Matrix models (Julian Hennicker, University of Geneva, Switzerland)

10.03.2020 14:00 – 15:00

Models that contain thin heterogeneous layers provide particular challanges for their numerical solution (meshing issues, badly conditioned Jacobian). Most prominently, such situations occur for flow through fractured porous media. In view of real life simulations, one might consider reduced models, which represent the fracture as a hypersurface embedded in the surrounding rock matrix. In the work, which I will present tomorrow, we introduce a completely new approach to develop and analyze reduced order elliptic PDE models on fractured domains. We use a Fourier analysis to obtain coupling conditions between matrix and fracture subdomains, for the reduced models. In a second step, we present error estimates for the reduced order models in terms of the fracture width, results that are still missing in the literature. For the proofs, we rely on a combination of Fourier analysis, asymptotic expansions and functional analysis. Finally, we study the behaviour of the error of the reduced order solutions on numerical test cases, when the fracture width tends to zero.

Lieu

Room 623, Séminaire d'analyse numérique

entrée libre