We present here the first results of a work on a multiscale resolution method using both Finite Volumes and Elements. Our method relies upon the coupling of grid scales: a coarse one and a fine one. The trick is to build a Finite Element basis on the coarse grid from problems solved on the fine one. In previous works on this subject [1] [2], the Finite Element method was used in both the fine a...

An affine finite element scheme approximation of a time dependent linear convectiondiffusion-reaction problem in 2D and 3D is presented. Specific conditions are given in terms of the coefficient functions, the computational grid and the discretization parameters to ensure that the nonnegativity property of the true solution is also satisfied by its approximation. Numerical examples are given wh...

Interpolation of field data from unstructured meshes requires the potentially expensive identification of the finite element or volume within which the interpolating point lies. A number of geometric search algorithms have been proposed to reduce this expense at the cost of setting up and storing additional search tables. Using tetrahedral finite element models we show that a structured auxilia...

A new procedure for accelerating the convergence of mixed finite element approximations of the eigenpairs and of the biharmonic operator is proposed. It is based on a postprocessing technique that involves an additional solution of a source problem on an augmented finite element space. This space could be obtained either by substantially refining the grid, the two-grid method, or by using the s...

A UK-based grid computing project that merges two earthquake data modeling methods is one of the latest tools in earthquake prediction. The new technique provides a 2D data map of tectonic structures by combining a macro modeling method based on surface deformation measurements from satellite imagery with a micro method based on finite element analysis and simulation within local geophysical co...

A multilevel homotopic adaptive finite element method is presented in this paper for convection dominated problems. By the homotopic method with respect to the diffusion parameter, the grids are iteratively adapted to better approximate the solution. Some new theoretic results and practical techniques for the grid adaptation are presented. Numerical experiments show that a standard finite eleme...

This paper presents a cell-based smoothed finite element method (CS-FEM) for solving two-dimensional contact problems with the bi-potential formulation. The force and relative displacements on surface are coupled each other. Uzawa algorithm, which is local iterative technique, used to solve force. classic Coulomb friction rule unilateral relationship considered. There no need select any user-de...

1. Abstract In this paper, we implement the extended finite element method (X-FEM) combined with the level set method to solve structural shape and topology optimization problems. Numerical comparisons with the conventional finite element method in a fixed grid show that the X-FEM leads to more accurate results without increasing the mesh density and the degrees of freedom. Furthermore, the mes...