On discrete functional inequalities for some finite volume schemes

We prove several discrete Gagliardo-Nirenberg-Sobolev and Poincar\'e-Sobolev inequalities for some approximations with arbitrary boundary values on finite volume meshes. The keypoint of our approach is to use the continuous embedding of the space $BV(\Omega)$ into $L^{N/(N-1)}(\Omega)$ for a Lipschitz domain $\Omega \subset \mathbb{R}^{N}$, with $N \geq 2$. Finally, we give several applications to discrete duality finite volume (DDFV) schemes which are used for the approximation of nonlinear and non isotropic elliptic and parabolic problems

Preserving monotony of combined edge finite volume–finite element scheme for a bone healing model on general mesh

International audienceIn this article, we propose and analyse a combined finite volume–finite element scheme for a bone healing model. This choice of discretization allows to take into account anisotropic diffusions without imposing any restrictions on the mesh. Moreover, following the work of C. Cancès et al. 2013, we define a nonlinear correction of the diffusive terms to obtain a monotone scheme. We provide, under a numerical assumption, a complete convergenceanalysis of this corrected scheme, and present some numerical experiments which show its good behavior

A finite volume scheme for convection-diffusion equations with nonlinear diffusion derived from the Scharfetter-Gummel scheme

International audienceWe propose a finite volume scheme for convection-diffusion equations with nonlinear diffusion. Such equations arise in numerous physical contexts. We will particularly focus on the drift-diffusion system for semiconductors and the porous media equation. In these two cases, it is shown that the transient solution converges to a steady-state solution as t tends to infinity. The introduced scheme is an extension of the Scharfetter-Gummel scheme for nonlinear diffusion. It remains valid in the degenerate case and preserves steady-states. We prove the convergence of the scheme in the nondegenerate case. Finally, we present some numerical simulations applied to the two physical models introduced and we underline the efficiency of the scheme to preserve long-time behavior of the solutions

When teaching style matches students' epistemic (in)dependence: The moderating effect of perceived epistemic gap

In a 2×2×2 factorial design, 3rd year Romanian psychology students (N=94) were assigned into 2 groups according to the extent to which they acknowledged an epistemic dependence (lowvs. high) toward their professor. They then compared the competence of 3rd year students to that of 1st year or 5th year students. Finally, they were exposed to a persuasive counter-attitudinal message from an epistemic authority, framed in an authoritarian vs. democratic style. The main dependent variable was the influence of the counter-attitudinal message. Results show an interaction between the three variables. No effects were found among students in the upward social comparison condition in which they felt particularly incompetent. The expected interaction between style and dependence was significant in the down ward comparison condition where participants felt more competent than 1st year students. Students high in perceived epistemic dependence were more influenced by the authoritarian style than those low in epistemic dependence. The reverse tended to be true for participants exposed to the democratic styl

The social transmission of knowledge at the University: Teaching style and epistemic dependence

It is argued that an epistemic authority would induce greater influence in transmitting knowledge to students when there is a correspondence between the (authoritarian vs. democratic) style of the authority and students' perceptions of their relation to the authority (high vs. low epistemic dependence). In two studies it was predicted, and found, that students who perceived themselves in a state of low epistemic dependence towards their teachers were more influenced by a democratic than by an authoritarian teaching style. This difference in appropriation was not found for students who perceived themselves in a state of epistemic dependence towards the epistemic authorit

Deflecting Stereotype Threat Through Downward Comparison: When Comparison with Immigrants Boosts the Performance of Stigmatized Native Students

Two experiments examined the effect of comparison with immigrants on the intellectual performance of stigmatized native students (i.e., women and students from low socioeconomic backgrounds). It was predicted that such a comparison may boost the test performance of both groups of students rather than comparison with their counterparts who are not stigmatized. In line with this hypothesis, we found that female European students (Study 1) performed better on a math test when they were led to compare with a female immigrant rather than with another female European student. Study 2 replicated this finding in regard to the performance of native students with low socioeconomic status on a general intelligence test. Results are discussed in terms of stereotype susceptibility predicaments and their implications for native-immigrant performance gap