GEM - International Journal on Geomathematics https://doi.org/10.1007/s13137-018-0105-3 ORIGINAL PAPER Advanced computation of steady-state fluid flow in Discrete Fracture-Matrix models: FEM–BEM and VEM–VEM fracture-block coupling S. Berrone 1 · A. Borio 1 · C. Fidelibus 2 · S. Pieraccini 3 · S. Scialò 1 · F. Vicini 1 Received: 31 March 2018 / Accepted: 18 July 2018 © Springer-Verlag GmbH Germany, part of Springer Nature 2018 Abstract In this note the issue of fluid flow computation in a Discrete Fracture-Matrix (DFM) model is addressed. In such a model, a network of percolative fractures delimits porous matrix blocks. Two frameworks are proposed for the coupling between the two media. First, a FEM–BEM technique is considered, in which finite elements on non-conforming grids are used on the fractures, whereas a boundary element method is used on the blocks; the coupling is pursued by a PDE-constrained optimization formulation of the problem. Second, a VEM–VEM technique is considered, in which a 2D and a 3D virtual element method are used on the fractures and on the blocks, respectively, taking advantage of the flexibility of VEM in using arbitrary meshes in order to ease the meshing process and the consequent enforcement of the matching conditions on fractures and blocks. Keywords Coupling 3D BEM–2D FEM · Optimization procedure for non-matching grids · Coupling 3D VEM–2D VEM · Conforming polygonal-polyhedral meshes · Steady-state flows in porofractured media · Dual-porosity media Mathematics Subject Classification 65N30 · 65N50 · 68U20 · 86-08 · 86A05 · 86A60 1 Introduction Two main approaches are available for the simulation of the fluid flow regime in poro-fractured media: the Dual-Porosity Continuum (DPC) and the Discrete Fracture- This research has been partially supported by INdAM-GNCS Project 2018, and by the MIUR project “Dipartimenti di Eccellenza 2018-2022”. Computational resources were partially provided by HPC@POLITO (http://hpc.polito.it) and by CINECA Project IsC58 HP10CDFLWH. Authors S.B., A.B., S.P., S.S., F.V. are members of the INdAM research group GNCS. Extended author information available on the last page of the article 123