[PDF] Top 20 Lp estimates for the homogenization of stokes problem in a perforated domain

... u in L p -spaces (for p < 6) up to the extraction of a ...herein in providing a quantitative estimate of the convergence of u N to ¯ ...This ... Voir le document complet

... independent of k, ρ k i and |F i k | are uniformly bounded from below in k and ...such a decomposition with N k and ρ k i independent of k and ...precise the dependance on the ... Voir le document complet

... to the forcing term in the Vlasov equation and the corresponding term ...(1.1) in the Navier-Stokes system is obtained by assuming that the forces induced by ... Voir le document complet

... Keywords: A posteriori error estimation, Navier-Stokes problem, iterative ...Introduction The a posteriori analysis controls the overall discretization error of a ... Voir le document complet

... given. The closely related problem of periodic homogenization of the Stokes equations in a bounded domain perforated by tiny holes is ... Voir le document complet

... proved in [2] for scalar valued func- tions f ∈ L 2 (Ω, R), and only the first part of a ([2, Proposition ...and the second part of b ([2, Proposition 3.5]) can be found ... Voir le document complet

... from the considerations of [4] for the implementation of the unfolding method in the case of perforated ...presents a brief summary of ... Voir le document complet

... 4.1. A level-set formulation 10 The level-set approach is a very convenient tool in shape identification, see [29] for a general introduction, or [30] where the approach ... Voir le document complet

... denotes the transpose operator. Notice that all the discussion below can be extended to more general boundary conditions, but we stick to the homogeneous Dirichlet case for simplicity ... Voir le document complet

... Moreover, the asymptotic estimates for t → ∞ given in Theorem ...have a limitation on the size of the data, which however only affects the atomic part ... Voir le document complet

... introduce a few general notations, we also give some recalls on lemmas, definitions and results about the unfolding method in periodic homogenization; this complements the paper which ... Voir le document complet

... regards the problem of stability, if the Steklov eigenvalues are known up to a positive, fixed and small ε, is it possible to find an approximation of the conformal factor ... Voir le document complet

... variant of these concentration inequalities plays an analogous role in this paper (see Proposition ...on the decay of the Green’s function for the heterogenous operator ... Voir le document complet

... on the Nitsche’s penalty parameter to be large enough. An improvement of the cell-agglomeration algorithm and numerical simulations were also ...provided. The present study extends the ... Voir le document complet

... Influence of the reaction parameter on the convergence (h = 1/96), (b) Influence of the mesh size for c = 10 − 5 ...see in Table 1(a) that the convergence ... Voir le document complet

... that the nuclear reactor core is periodic, i.e. all coe¯ cients A(y), § (y) and ¼ (y) are Y -periodic ...crucial for the homogenization procedure. In particular, our results do ... Voir le document complet

... give a short outline of the paper. In Section 2 we introduce the Stokes equa- ...on the two-dimensional case, these equations are transformed to a bi-harmonic ... Voir le document complet

... formed in [7] ...convergence for the three fields in L 2 - norm: Oðh 2 Þ for the vorticity, OðhÞ for velocity and pres- ...approached. In particular, on a ... Voir le document complet

... performed in two steps. First, we use Fourier truncation, i.e. we only solve a finite number of two-dimensional problems and recall the estimate of the corresponding error from ... Voir le document complet

... are in a situation which is analogue to Case 1 above but we remark that, for the trajectory, the cost to go from 0 to 1 and then from 1 to 2 [or from 0 to −1 and then from −1 to −2] is ... Voir le document complet