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The aim of this paper is to give a simple, introductory presentation of the extension of the Virtual Element Method to the discretization of H(div)-conforming vector fields (or, more generally, of (n − 1) − Cochains). As we shall see, the methods presented here can be seen as extensions of the so-called BDM family to deal with more general element geometries (such as polygons with an almost arbitrary geometry). For the sake of simplicity, we limit ourselves to the 2-dimensional case, with the aim...
The dynamical investigation of two-component poroelastic media is important for practical applications. Analytic solution methods are often not available since they are too complicated for the complex governing sets of equations. For this reason, often some existing numerical methods are used. In this work results obtained with the finite element method are opposed to those obtained by Schanz using the boundary element method. Not only the influence of the number of elements and time steps on the...
Ω being a bounded open set in R∙, with regular boundary, we associate with Navier-Stokes equation in Ω where the velocity is null on ∂Ω, a non-linear branching process (Yt, t ≥ 0). More precisely: Eω0(〈h,Yt〉) = 〈ω,h〉, for any test function h, where ω = rot u, u denotes the velocity solution of Navier-Stokes equation. The support of the random measure Yt increases or decreases in one unit when the underlying process hits ∂Ω; this stochastic phenomenon corresponds to the creation-annihilation of vortex...
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