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On the remainder in the Weyl formula for the Euclidean disk

Yves Colin de Verdière (2010/2011)

Séminaire de théorie spectrale et géométrie

We prove a 2-terms Weyl formula for the counting function N ( μ ) of the spectrum of the Laplace operator in the Euclidean disk with a sharp remainder estimate O μ 2 / 3 .

On the Schwarz algorithms for the elliptic exterior boundary value problems

Faker Ben Belgacem, Miche Fournié, Nabil Gmati, Faten Jelassi (2005)

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

Tuning the alternating Schwarz method to the exterior problems is the subject of this paper. We present the original algorithm and we propose a modification of it, so that the solution of the subproblem involving the condition at infinity has an explicit integral representation formulas while the solution of the other subproblem, set in a bounded domain, is approximated by classical variational methods. We investigate many of the advantages of the new Schwarz approach: a geometrical convergence...

On the Schwarz algorithms for the Elliptic Exterior Boundary Value Problems

Faker Ben Belgacem, Michel Fournié, Nabil Gmati, Faten Jelassi (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

Tuning the alternating Schwarz method to the exterior problems is the subject of this paper. We present the original algorithm and we propose a modification of it, so that the solution of the subproblem involving the condition at infinity has an explicit integral representation formulas while the solution of the other subproblem, set in a bounded domain, is approximated by classical variational methods. We investigate many of the advantages of the new Schwarz approach: a geometrical convergence...

On the second-order convergence of a function reconstructed from finite volume approximations of the Laplace equation on Delaunay-Voronoi meshes

Pascal Omnes (2011)

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

Cell-centered and vertex-centered finite volume schemes for the Laplace equation with homogeneous Dirichlet boundary conditions are considered on a triangular mesh and on the Voronoi diagram associated to its vertices. A broken P1 function is constructed from the solutions of both schemes. When the domain is two-dimensional polygonal convex, it is shown that this reconstruction converges with second-order accuracy towards the exact solution in the L2 norm, under the sufficient condition that the...

On the second-order convergence of a function reconstructed from finite volume approximations of the Laplace equation on Delaunay-Voronoi meshes

Pascal Omnes (2011)

ESAIM: Mathematical Modelling and Numerical Analysis

Cell-centered and vertex-centered finite volume schemes for the Laplace equation with homogeneous Dirichlet boundary conditions are considered on a triangular mesh and on the Voronoi diagram associated to its vertices. A broken P1 function is constructed from the solutions of both schemes. When the domain is two-dimensional polygonal convex, it is shown that this reconstruction converges with second-order accuracy towards the exact solution in the L2 norm, under the sufficient condition that the...

On the solution of a generalized system of von Kármán equations

Jozef Kačur (1981)

Aplikace matematiky

A nonlinear system of equations generalizing von Kármán equations is studied. The existence of a solution is proved and the relation between the solutions of the considered system and the solutions of von Kármán system is studied. The system considered is derived in a former paper by Lepig under the assumption of a nonlinear relation between the intensity of stresses and deformations in the constitutive law.

On the solution of some non-local problems

F. Criado, Jr. Criado, F., N. Odishelidze (2004)

Czechoslovak Mathematical Journal

This paper deals with two types of non-local problems for the Poisson equation in the disc. The first of them deals with the situation when the function value on the circle is given as a combination of unknown function values in the disc. The other type deals with the situation when a combination of the value of the function and its derivative by radius on the circle are given as a combination of unknown function values in the disc. The existence and uniqueness of the classical solution of these...

On the traces of W2,p(Ω) for a Lipschitz domain.

Ricardo G. Durán, María Amelia Muschietti (2001)

Revista Matemática Complutense

We extend to the case 1 < p the results obtained by Geymonat and Krasucki for p = 2 on the characterization of the traces of W2,p(Ω) for a bounded Lipschitz domain.

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