Convergence d'un schéma itératif explicite

Laydi, Mohamed Rachid

doi:10.1016/s0764-4442(97)89801-1

Cited by 2 publications

(1 citation statement)

References 6 publications

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“…Note in particular that the sum which defines V H h is, a priori, not a direct sum. This property makes the above algorithm different from most known iterative schemes (see for example the scheme by Laydi [26]). The algorithm resembles the FAC method, see for example the works from McCormick et al [29][30][31], or possibly a hierarchical method (see for example the papers from Yserentant [44,45], Bank et al [10] and Bank and Smith [11]) with a mortar method (see [2]).…”

Section: Algorithm 1 1 Setmentioning

confidence: 96%

Finite element approximation of multi-scale elliptic problems using patches of elements

Glowinski

Lozinski

et al. 2005

Numer. Math.

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In this paper we present a method for the numerical solution of elliptic problems with multi-scale data using multiple levels of not necessarily nested grids. The method consists in calculating successive corrections to the solution in patches whose discretizations are not necessarily conforming. This paper provides proofs of the results published earlier (see C. R. Acad. Sci. Paris, Ser. I 337 (2003) 679-684), gives a generalization of the latter to more than two domains and contains extensive numerical illustrations. New results including the spectral analysis of the iteration operator and a numerical method to evaluate the constant of the strengthened Cauchy-Buniakowski-Schwarz inequality are presented. Mathematics Subject Classifications (1991) 65N55 · 65N30 · 65N12

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Section: Algorithm 1 1 Setmentioning

confidence: 96%

Finite element approximation of multi-scale elliptic problems using patches of elements

Glowinski

Lozinski

et al. 2005

Numer. Math.

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Tensioactive Properties of Semidilute Polymer Solutions

Manghi

Aubouy

2000

Macromolecules

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We present a scaling description of adsorbed polymer layers in the presence of a semidilute solution. Within a very simple model where the layer is treated as a thermodynamic ensemble of loops with a large polydispersity in size, we are able to (a) describe the influence of the semidilute solution on the structure of the layer of adsorbed chains, and (b) estimate the variation of the surface tension γ of the solution as a function of the polymerization index of the chains (N) and the monomer volume fraction in the bulk (Φb). Concerning point a, this work provides a continuous picture for the variations of the static properties of the interfacial layer from the dilute case (Φb → 0), to the melt case (Φb → 1). Concerning point b, we find a law γ(Φb, N) of the form (good solvent conditions) γVdW − AΦb 5/4 + B(Φb 7/8/N 1/2) ln(N/Φb 7/12 N*), where γVdW accounts for van der Waals interactions and N* is a characteristic index of polymerization of the polymer under consideration (A and B are calculated within numerical coefficients of order unity). This law is in good quantitative agreement with experimental measurements and generalizes our recent findings on the case of molten polymer liquid. (Aubouy; Manghi; Raphaël. Phys. Rev. Lett. 2000, 84, 4858.)

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Convergence d'un schéma itératif explicite

Cited by 2 publications

References 6 publications

Finite element approximation of multi-scale elliptic problems using patches of elements

Finite element approximation of multi-scale elliptic problems using patches of elements

Tensioactive Properties of Semidilute Polymer Solutions

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