Enhanced RFB method

The residual-free bubble method (RFB) is a parameter-free stable finite element method that has been applied successfully to solve a wide range of boundary-value problems presenting multiple-scale behavior. If some local features of the solution are known a-priori, the RFB finite element space approximation properties can be increased by enriching it on some specific edges of the partition (see[7]). Based on such idea, we define and analyse the enhanced residual-free bubbles method for the solution of convection-dominated convection-diffusion problems in 2-D. Our a-priori analysis enlightens the limitations of the RFB method and the superior global convergence properties of the new method. The theoretical results are supported by extensive numerical experimentation.\ud \ud The first author acknowledges the financial support of INdAM and EPSR

Conforming and nonconforming virtual element methods for elliptic problems

We present in a unified framework new conforming and nonconforming Virtual Element Methods (VEM) for general second order elliptic problems in two and three dimensions. The differential operator is split into its symmetric and non-symmetric parts and conditions for stability and accuracy on their discrete counterparts are established. These conditions are shown to lead to optimal $H^1$- and $L^2$-error estimates, confirmed by numerical experiments on a set of polygonal meshes. The accuracy of the numerical approximation provided by the two methods is shown to be comparable

Discontinuous Galerkin Methods for Mass Transfer through Semi-Permeable Membranes

A discontinuous Galerkin (dG) method for the numerical solution of initial/boundary value multi-compartment partial differential equation (PDE) models, interconnected with interface conditions, is presented and analysed. The study of interface problems is motivated by models of mass transfer of solutes through semi-permeable membranes. More specifically, a model problem consisting of a system of semilinear parabolic advection-diffusion-reaction partial differential equations in each compartment, equipped with respective initial and boundary conditions, is considered. Nonlinear interface conditions modelling selective permeability, congestion and partial reflection are applied to the compartment interfaces. An interior penalty dG method is presented for this problem and it is analysed in the space-discrete setting. The a priori analysis shows that the method yields optimal a priori bounds, provided the exact solution is sufficiently smooth. Numerical experiments indicate agreement with the theoretical bounds and highlight the stability of the numerical method in the advection-dominated regime

Karl Polanyi : breve biografia intellettuale

"Les grandes étapes de la vie et de la carrière de Polanyi, ainsi que la genèse de ses principales idées, sont retracées dans ce texte. Son oeuvre, qui fut profondément marquée par l'idéal socialiste et la lecture de Marx, s'inscrit dans la première partie du XXe siècle, marquée par la survenue de catastrophes majeures et par l'effacement d'une première société de marché qui a pris forme au XIXe siècle. Ces grandes ruptures constituent le défi intellectuel auquel il tente de répondre. Il montre que la volonté de créer, au XIXe siècle, un grand marché autorégulateur exprime une mutation de l'ordre culturel occidental qui prétend réduire la terre, le travail et la monnaie à autant de marchandises. L'économie de marché se différencie des nombreuses économies du passé qui ont connu des marchés, mais dont l'articulation ne constituait pas le système du Grand Marché que nous connaissons depuis la Révolution industrielle"La vita di Polanyi fu effettivamente segnata dalle vicende che sconvol sero il mondo, tra la fine del XIX secolo (era nato nel 1886) e la prima metà del XX. Le sue tre (o quattro, come vedremo) emigrazioni dipesero, direttamente o indirettamente, motivi politici..