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Displaying 141 –
156 of
156
The main goal of this article is to establish a priori and a posteriori
error estimates for the numerical approximation of some non linear elliptic
problems arising in glaciology. The stationary motion of a glacier is given
by a non-Newtonian fluid flow model which becomes, in a first
two-dimensional approximation, the so-called infinite parallel sided slab
model. The approximation of this model is made by a finite element method
with piecewise polynomial functions of degree 1. Numerical results...
By means of eigenvalue error expansion and integral expansion techniques, we propose and analyze the stream function-vorticity-pressure method for the eigenvalue problem associated with the Stokes equations on the unit square. We obtain an optimal order of convergence for eigenvalues and eigenfuctions. Furthermore, for the bilinear finite element space, we derive asymptotic expansions of the eigenvalue error, an efficient extrapolation and an a posteriori error estimate for the eigenvalue. Finally,...
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 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...
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 flow of a viscous incompressible fluid in a rigid homogeneous porous medium provided with mixed boundary conditions. Since the boundary pressure can present high variations, the permeability of the medium also depends on the pressure, so that the model is nonlinear. A posteriori estimates allow us to omit this dependence where the pressure does not vary too much. We perform the numerical analysis of a spectral element discretization of the simplified model. Finally we propose a strategy...
An averaging method for the second-order approximation of the values of the gradient of an arbitrary smooth function u = u(x 1, x 2) at the vertices of a regular triangulation T h composed both of rectangles and triangles is presented. The method assumes that only the interpolant Πh[u] of u in the finite element space of the linear triangular and bilinear rectangular finite elements from T h is known. A complete analysis of this method is an extension of the complete analysis concerning the finite...
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