Fibered microstructures for some nonlocal Dirichlet forms
Finite difference discretization of the Kuramoto-Sivashinsky equation.
Finite difference methods for coupled flow interaction transport models.
Finite difference solution of radiation effects on MHD unsteady free-convection flow over vertical plate with variable surface temperature.
Finite differences and boundary element methods for non-stationary viscous incompressible flow
We consider an implicit fractional step procedure for the time discretization of the non-stationary Stokes equations in smoothly bounded domains of ℝ³. We prove optimal convergence properties uniformly in time in a scale of Sobolev spaces, under a certain regularity of the solution. We develop a representation for the solution of the discretized equations in the form of potentials and the uniquely determined solution of some system of boundary integral equations. For the numerical computation of...
Finite element analysis of a simplified stochastic Hookean dumbbells model arising from viscoelastic flows
A simplified stochastic Hookean dumbbells model arising from viscoelastic flows is considered, the convective terms being disregarded. A finite element discretization in space is proposed. Existence of the numerical solution is proved for small data, so as a priori error estimates, using an implicit function theorem and regularity results obtained in [Bonito et al., J. Evol. Equ.6 (2006) 381–398] for the solution of the continuous problem. A posteriori error estimates are also derived. Numerical...
Finite element approximation of a free boundary problem arising in the theory of liquid drops ans plasma physics
Finite element approximation of a two-layered liquid film in the presence of insoluble surfactants
We consider a system of degenerate parabolic equations modelling a thin film, consisting of two layers of immiscible Newtonian liquids, on a solid horizontal substrate. In addition, the model includes the presence of insoluble surfactants on both the free liquid-liquid and liquid-air interfaces, and the presence of both attractive and repulsive van der Waals forces in terms of the heights of the two layers. We show that this system formally satisfies a Lyapunov structure, and a second energy...
Finite element approximation of incompressible Navier-Stokes equations with slip boundary condition II.
Finite element approximation of kinetic dilute polymer models with microscopic cut-off
We construct a Galerkin finite element method for the numerical approximation of weak solutions to a coupled microscopic-macroscopic bead-spring model that arises from the kinetic theory of dilute solutions of polymeric liquids with noninteracting polymer chains. The model consists of the unsteady incompressible Navier–Stokes equations in a bounded domain Ω ⊂ ,d= 2 or 3, for the velocity and the pressure of the fluid, with an elastic extra-stress tensor as right-hand side in the momentum equation....
Finite element approximation of kinetic dilute polymer models with microscopic cut-off
We construct a Galerkin finite element method for the numerical approximation of weak solutions to a coupled microscopic-macroscopic bead-spring model that arises from the kinetic theory of dilute solutions of polymeric liquids with noninteracting polymer chains. The model consists of the unsteady incompressible Navier–Stokes equations in a bounded domain Ω ⊂ , d = 2 or 3, for the velocity and the pressure of the fluid, with an elastic extra-stress tensor as right-hand side in the momentum equation....
Finite element approximation of the Navier-Stokes equation.
Finite element approximations for the stationary large eddy simulation model
Some approximation procedures are presented for the system of equations arising from the large eddy simulation of turbulent flows. Existence of solutions to the approximate problems is proved. Discrete solutions generate a strongly convergent subsequence whose limit is a weak solution of the original problem. To prove the convergence theorem we use Young measures and related tools. We do not limit ourselves to divergence-free functions and our results are in particular valid for finite element approximations...
Finite element discretization of Darcy's equations with pressure dependent porosity
We consider the flow of a viscous incompressible fluid through a rigid homogeneous porous medium. The permeability of the medium depends on the pressure, so that the model is nonlinear. We propose a finite element discretization of this problem and, in the case where the dependence on the pressure is bounded from above and below, we prove its convergence to the solution and propose an algorithm to solve the discrete system. In the case where the dependence on the pressure is exponential, we propose...
Finite element error analysis of a quasi-Newtonian flow obeying the Carreau or power law.
Finite element in modeling of flow in porous media: How to describe wells.
Finite element methods for the three-field Stokes system in : Galerkin methods
Finite element solution of flows through cascades of profiles in a layer of variable thickness
The paper is devoted to the numerical modelling of a subsonic irrotational nonviscous flow past a cascade of profiles in a variable thickness fluid layer. It leads to a nonlinear two-dimensional elliptic problem with nonstandard nonhomogeneous boundary conditions. The problem is discretized by the finite element method. Both theoretical and practical questions of the finite element implementation are studied; convergence of the method, numerical integration, iterative methods for the solution of...
Finite element solution of Navier-Stokes equations in shallow domains
Finite elemnt approximation of viscoelastic fluid flow: Existence of approximate solutions and error bounds.