778 research outputs found
Convergence of finite volume scheme for degenerate parabolic problem with zero flux boundary condition
This note is devoted to the study of the finite volume methods used in the discretization of degenerate parabolic-hyperbolic equation with zero-flux boundary condition. The notion of an entropy-process solution, successfully used for the Dirichlet problem, is insufficient to obtain a uniqueness and convergence result because of a lack of regularity of solutions on the boundary. We infer the uniqueness of an entropy-process solution using the tool of the nonlinear semigroup theory by passing to the new abstract notion of integral-process solution. Then, we prove that numerical solution converges to the unique entropy solution as the mesh size tends to 0
Coupling techniques for nonlinear hyperbolic equations. III. The well-balanced approximation of thick interfaces
We continue our analysis of the coupling between nonlinear hyperbolic
problems across possibly resonant interfaces. In the first two parts of this
series, we introduced a new framework for coupling problems which is based on
the so-called thin interface model and uses an augmented formulation and an
additional unknown for the interface location; this framework has the advantage
of avoiding any explicit modeling of the interface structure. In the present
paper, we pursue our investigation of the augmented formulation and we
introduce a new coupling framework which is now based on the so-called thick
interface model. For scalar nonlinear hyperbolic equations in one space
variable, we observe that the Cauchy problem is well-posed. Then, our main
achievement in the present paper is the design of a new well-balanced finite
volume scheme which is adapted to the thick interface model, together with a
proof of its convergence toward the unique entropy solution (for a broad class
of nonlinear hyperbolic equations). Due to the presence of a possibly resonant
interface, the standard technique based on a total variation estimate does not
apply, and DiPerna's uniqueness theorem must be used. Following a method
proposed by Coquel and LeFloch, our proof relies on discrete entropy
inequalities for the coupling problem and an estimate of the discrete entropy
dissipation in the proposed scheme.Comment: 21 page
A finite volume scheme for nonlinear degenerate parabolic equations
We propose a second order finite volume scheme for nonlinear degenerate
parabolic equations. For some of these models (porous media equation,
drift-diffusion system for semiconductors, ...) it has been proved that the
transient solution converges to a steady-state when time goes to infinity. The
present scheme preserves steady-states and provides a satisfying long-time
behavior. Moreover, it remains valid and second-order accurate in space even in
the degenerate case. After describing the numerical scheme, we present several
numerical results which confirm the high-order accuracy in various regime
degenerate and non degenerate cases and underline the efficiency to preserve
the large-time asymptotic
Éducation thérapeutique du patient. Modèles, pratiques et évaluation
International audienceIssu d’une collaboration entre l’Inpes et des acteurs de l’éducation thérapeutique du patient, cet ouvrage rassemble des analyses d’interventions d’éducation thérapeutique mises en place en France et au Québec, dans le cadre de huit maladies chroniques : diabète, obésité, maladies cardio-vasculaires, VIH/sida, asthme, cancer, polyarthrite rhumatoïde et lombalgie. En rendant compte des modèles théoriques qui sous-tendent l’éducation thérapeutique et des démarches mises en œuvre, les contributions mettent au jour une large diversité de pratiques. Qu’il soit professionnel de santé, formateur ou chercheur, le lecteur trouvera ainsi des pistes pour démarrer, développer et évaluer ses actions éducatives. Il trouvera aussi matière à éprouver ses conceptions de la santé et de l’éducation, notamment à travers la découverte de pratiques qui produisent des résultats très encourageants alors qu’elles se réfèrent à des cadres théoriques diversifiés et à des voies différenciées pour penser l’action éducative.Parce qu’elles ne montrent pas l’excellence d’une voie plutôt qu’une autre, ces analyses invitent au développement de nouvelles perspectives d’action et de recherche. L’ouvrage offre ainsi une ouverture précieuse dans un contexte général où l’éducation thérapeutique s’inscrit dans le Code de santé publique, notamment à travers la loi Hôpital, patients, santé et territoires du 21 juillet 2009, qui en reconnaît l’importance pour l’amélioration de l’état de santé des personnes, en particulier de celles atteintes d’une maladie chronique
Piecewise linear transformation in diffusive flux discretization
To ensure the discrete maximum principle or solution positivity in finite
volume schemes, diffusive flux is sometimes discretized as a conical
combination of finite differences. Such a combination may be impossible to
construct along material discontinuities using only cell concentration values.
This is often resolved by introducing auxiliary node, edge, or face
concentration values that are explicitly interpolated from the surrounding cell
concentrations. We propose to discretize the diffusive flux after applying a
local piecewise linear coordinate transformation that effectively removes the
discontinuities. The resulting scheme does not need any auxiliary
concentrations and is therefore remarkably simpler, while being second-order
accurate under the assumption that the structure of the domain is locally
layered.Comment: 11 pages, 1 figures, preprint submitted to Journal of Computational
Physic
How much larger quantum correlations are than classical ones
Considering as distance between two two-party correlations the minimum number
of half local results one party must toggle in order to turn one correlation
into the other, we show that the volume of the set of physically obtainable
correlations in the Einstein-Podolsky-Rosen-Bell scenario is (3 pi/8)^2 = 1.388
larger than the volume of the set of correlations obtainable in local
deterministic or probabilistic hidden-variable theories, but is only 3 pi^2/32
= 0.925 of the volume allowed by arbitrary causal (i.e., no-signaling)
theories.Comment: REVTeX4, 6 page
On the bounded cohomology of semi-simple groups, S-arithmetic groups and products
We prove vanishing results for Lie groups and algebraic groups (over any
local field) in bounded cohomology. The main result is a vanishing below twice
the rank for semi-simple groups. Related rigidity results are established for
S-arithmetic groups and groups over global fields. We also establish vanishing
and cohomological rigidity results for products of general locally compact
groups and their lattices
Probabilistic analysis of the upwind scheme for transport
We provide a probabilistic analysis of the upwind scheme for
multi-dimensional transport equations. We associate a Markov chain with the
numerical scheme and then obtain a backward representation formula of
Kolmogorov type for the numerical solution. We then understand that the error
induced by the scheme is governed by the fluctuations of the Markov chain
around the characteristics of the flow. We show, in various situations, that
the fluctuations are of diffusive type. As a by-product, we prove that the
scheme is of order 1/2 for an initial datum in BV and of order 1/2-a, for all
a>0, for a Lipschitz continuous initial datum. Our analysis provides a new
interpretation of the numerical diffusion phenomenon
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