We consider a general loaded arch problem with a small thickness. To approximate the solution of this problem, a conforming mixed finite element method which takes into account an approximation of the middle line of the arch is given. But for a very small thickness such a method gives poor error bounds. the conforming Galerkin method is then enriched with residual-free bubble functions.
We analyze an isoparametric finite element method to compute the vibration modes of a plate, modeled by Reissner-Mindlin equations, in contact with a compressible fluid, described in terms of displacement variables. To avoid locking in the plate, we consider a low-order method of the so called MITC (Mixed Interpolation of Tensorial Component) family on quadrilateral meshes. To avoid spurious modes in the fluid, we use a low-order hexahedral Raviart-Thomas elements and a non conforming coupling is...
We analyze an isoparametric finite element method to compute the vibration modes of a plate, modeled by Reissner-Mindlin equations, in contact with a compressible fluid, described in terms of displacement variables. To avoid locking in the plate, we consider a low-order method of the so called MITC (Mixed Interpolation of Tensorial Component) family on quadrilateral meshes. To avoid spurious modes in the fluid, we use a low-order hexahedral Raviart-Thomas elements and a non conforming coupling...
We consider in all curvature equation where G is a nondecreasing function and curv(u) is the curvature of the level line passing by x. These equations are invariant with respect to any contrast change u → g(u), with g nondecreasing. Consider the contrast invariant operator . A Matheron theorem asserts that all contrast invariant operator T can be put in a form . We show the asymptotic equivalence of both formulations. More precisely, we show that all curvature equations can be obtained...
The paper is a contribution to the complex variable boundary element method, shortly CVBEM. It is focused on Jordan regions having piecewise regular boundaries without cusps. Dini continuous densities whose modulus of continuity satisfies are considered on these boundaries. Functions satisfying the Hölder condition of order , , belong to them. The statement that any Cauchy-type integral with such a density can be uniformly approximated by a Cauchy-type integral whose density is a piecewise...
This study concerns some asymptotic models used to compute the flow outside and inside fractures in a bidimensional porous medium. The flow is governed by the Darcy law both in the fractures and in the porous matrix with large discontinuities in the permeability tensor. These fractures are supposed to have a small thickness with respect to the macroscopic length scale, so that we can asymptotically reduce them to immersed polygonal fault interfaces and the model finally consists in a coupling between...
We consider the problem of minimising the nth-eigenvalue of the Robin Laplacian in RN. Although for n = 1,2 and a positive boundary parameter α it is known that the minimisers do not depend on α, we demonstrate numerically that this will not always be the case and illustrate how the optimiser will depend on α. We derive a Wolf–Keller type result for this problem and show that optimal eigenvalues grow at most with n1/N, which is in sharp contrast with the Weyl asymptotics for a fixed domain. We further...
In this paper, using a new correction to the Crouzeix-Raviart finite element eigenvalue approximations, we obtain asymptotic lower bounds of eigenvalues for the Steklov eigenvalue problem with variable coefficients on -dimensional domains (). In addition, we prove that the corrected eigenvalues converge to the exact ones from below. The new result removes the conditions of eigenfunction being singular and eigenvalue being large enough, which are usually required in the existing arguments about...