Florence Hubert

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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)
— We present a detailed survey of discrete functional analysis tools (consistency results, Poincaré and Sobolev embedding inequalities, discrete W 1,p compactness, discrete compactness in space and in time) for the so-called Discrete Duality (DDFV) Finite Volume schemes in three space dimensions. We concentrate mainly on the 3D CeVe-DDFV scheme presented in(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)
This paper provides a new fully discrete domain decomposition algorithm for the advection diffusion reaction equation. It relies on the optimized Ventcell–Schwarz algorithm with a finite volume discretization of the subdomain problems. The scheme includes a wide range of advection fluxes with a special treatment on the boundary. A complete analysis of the(More)
A mathematical model for time development of metastases and their distribution in size and carrying capacity is presented. The model is used to theoretically investigate anti-­‐cancer therapies such as surgery and chemical treatments (cytotoxic or anti-­‐angiogenic), in monotherapy or in combination. Quantification of the effect of surgery on the size(More)
The case A 31-year-oldwoman (Figure 1: III-1) was evaluated for mild renal failure. The serum creatinine was 1.5 mg/dL and the creatinine clearance 55 mL/min (Cockcroft formula). The blood urea nitrogen and urate levels were 52 and 4.8 mg/dL, respectively. There was a mild microalbumin-uria (57 mg/24 h); urinalysis was unremarkable. Renal ul-trasonography(More)
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