*Correspondence: [email protected] Department of Mathematics, Azarbaijan Shahid Madani University, Tabriz, Iran Full list of author information is available at the end of the article Abstract By making a special product Banach space and using the famous result of Covitz and Nadler on fixed point of multifunctions we investigate the existence of a solution for a system of fractional finite ...

A finite element method with an adaptive mesh redistribution technique is presented for solving the Kohn-Sham equation. The mesh redistribution strategy is based on the harmonic mapping, and the movement of grid points is partially controlled by the monitor function that depends on the gradient of the electron density. Compared with fixed meshes, both efficiency and accuracy of the solution are...

The Finite Element Method (FEM) has become the standard tool for the analysis of a wide range of mechanical problems. However, the classical FEM is not well suited for the treatment of large deformation problems since excessive mesh distortions require remeshing. The Material Point Method (MPM) represents an approach in which material points moving through a fixed finite element grid are used t...

The paper presents a convergence analysis of a multigrid solver for a system of linear algebraic equations resulting from the discretization of a convection-diffusion problem using a finite element method. We consider piecewise linear finite elements in combination with a streamline diffusion stabilization. We analyze a multigrid method that is based on canonical intergrid transfer operators, a...

n this work, computational fluid dynamics of the flow behavior in a cold flow of fluidized bed is studied. An improved finite volume based finite element method has been introduced to solve the two-phase gas/solid flow hydrodynamic equations. This method uses a collocated grid, where all variables are located at the nodal points. The fluid dynamic model for gas/solid two-phase flow is based on ...

In this paper, we analyze a scheme for the time-dependent variable density Navier-Stokes equations. The algorithm is implicit in time, and the space approximation is based on a low-order staggered non-conforming finite element, the so-called Rannacher-Turek element. The convection term in the momentum balance equation is discretized by a finite volume technique, in such a way that a solution ob...

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...