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We present here a number of test cases and meshes which were designed to form a benchmark for finite volume schemes and give a summary of some of the results which were presented by the participants to this benchmark. We address a two-dimensional anisotropic diffusion problem, which is discretized on general, possibly non-conforming meshes. In most cases,(More)
Discrete Duality Finite Volume (DDFV) schemes have recently been developed in 2D to approximate nonlinear diffusion problems on general meshes. In this paper, a 3D extension of these schemes is proposed. The construction of this extension is detailed and its main properties are proved: a priori bounds, well-posedness and error estimates. The practical(More)
This paper investigates the impact of inward investment by foreign-owned companies on technical progress and hence labour productivity in the UK manufacturing sector. Using an industry-level panel data set we find that foreign-owned firms have a significant positive effect on the level of technical efficiency in domestic firms. There is evidence of(More)
This study concerns some asymptotic models used to compute the flow outside and inside fractures in a bidimensional porous medium. The flow is governed by the Darcy law both in the fractures and in the porous matrix with large discontinuities in the permeability tensor. These fractures are supposed to have a small thickness with respect to the macroscopic(More)
Defining tumor stage at diagnosis is a pivotal point for clinical decisions about patient treatment strategies. In this respect, early detection of occult metastasis invisible to current imaging methods would have a major impact on best care and long-term survival. Mathematical models that describe metastatic spreading might estimate the risk of metastasis(More)
We propose a new finite volume scheme for convection diffusion equation on non matching grids. We give error estimates for H 2 solutions of the continuous problem. We then present a finite volume version of an adaptation of the Schwarz algorithm due to P.L. Lions, and prove, for a fixed mesh, its convergence towards the finite volume scheme on the whole(More)
This article is concerned with the analysis of semi-discrete-in-space and fully-discrete approximations of the null controllability (and controllability to the trajectories) for parabolic equations. We propose an abstract setting for space discretizations that potentially encompasses various numerical methods and we study how the controllability problems(More)