The most challenging issue in performing underground flow simulations in Discrete Fracture Networks (DFN), is to effectively tackle the geometrical difficulties of the problem. In this work we put forward a new application of the Virtual Element Method combined with the Mortar method for domain decomposition: we exploit the flexibility of the VEM in handling polygonal meshes in order to easily construct meshes conforming to the traces on each fracture, and we resort to the mortar approach in order to "weakly" impose continuity of the solution on intersecting fractures. The resulting method replaces the need for matching grids between fractures, so that the meshing process can be performed independently for each fracture. Numerical results show optimal convergence and robustness in handling very complex geometries.

In this paper we propose a modified construction for the polynomial basis on polygons used in the Virtual Element Method (VEM). This construction is alternative to the classical monomial basis used in the classical construction of the VEM and is designed in order to improve numerical stability. For badly shaped elements the construction of the projection matrices required for assembling the local coefficients of the linear system within the VEM discretization of Partial Differential Equations can result very ill conditioned. The proposed approach can be easily implemented within an existing VEM code in order to reduce the possible ill conditioning of the elemental projection matrices. Numerical results applied to an hydro-geological flow simulation that often produce very badly shaped elements show a clear improvement of the quality of the numerical solution, confirming the viability of the approach. The method can be conveniently combined with a classical implementation of the VEM and applied element-wise, thus requiring a rather moderate additional numerical cost.

In the framework of the discretization of advection-diffusion problems by means of the Virtual Element Method, we consider stabilization issues. Herein, stabilization is pursued by adding a consistent SUPG-like term. For this approach we prove optimal rates of convergence. Numerical results clearly show the stabilizing effect of the method up to very large Péclet numbers and are in very good agreement with the expected rate of convergence.

A residual-based a posteriori error estimate for the Poisson problem with discontinuous diffusivity coefficient is derived in the case of a virtual element discretization. The error is measured considering a suitable polynomial projection of the discrete solution to prove an equivalence between the defined error and a computable residual based error estimator that does not involve any term related to the virtual element stabilization. Numerical results display a very good behavior of the ratio between the error and the error estimator, resulting independent of the meshsize and element distortion.

The paper is considering an opportunity for the CERN/GranSasso (CNGS) neutrino complex, concurrent time-wise with T2K and NOvA projects, with the aim of improving the sensitivity on v(mu) <-> v(e) theta(13) mixing angle by nearly an order of magnitude with respect to T2K expectations. The experiment is based on approximate to 20 kt fiducial volume LAr-TPC, following very closely the technology developed for the ICARUS-T600. The present preliminary proposal, called MODULAr, is focused on the following three main activities, for which we seek an extended international collaboration: (1) The neutrino beam from the CERN 400 GeV proton beam and an optimized horn focussing, eventually with an increased intensity in the framework of the LHC accelerator improvement programme. (2) A new experimental area LNGS-B, of at least 50,000 m(3) at 10 km off-axis from the main laboratory, eventually upgradable to larger sizes. A location is under consideration at about 1.2 km equivalent water depth. The bubble chamber like imaging and the very fine calorimetry of the LAr-TPC detector will ensure the best background recognition not only from the off-axis neutrinos from the CNGS but also for proton decay and cosmic neutrinos. (3) A new LAr Imaging detector, at least initially with about 20 kt fiducial mass, realised with a modular set of four identical, but independent units, each of about 5 kt, "cloning" the basic technology of the T600. Further phases may foresee extensions of MODULAr to a mass required by the future physics goals. Compared with large water Cherenkov (T2K) and fine grained scintillators (NOvA), the LAr-TPC offers a higher detection efficiency for a given mass and lower backgrounds, since virtually all channels may be unambiguously recognized. In addition to the search for 013 oscillations and CP violation, it would be possible to collect a large number of accurately identified cosmic ray neutrino events and perform search for proton decay in the exotic channels. (C) 2008 Elsevier B.V. All rights reserved