A Variational Finite Element Discretization of Compressible Flow

A Convergent Nonconforming Finite Element Method for Compressible Stokes Flow

We propose a nonconforming finite element method for isentropic viscous gas flow in situations where convective effects may be neglected. We approximate the continuity equation by a piecewise constant discontinuous Galerkin method. The velocity (momentum) equation is approximated by a finite element method on div–curl form using the nonconforming Crouzeix– Raviart space. Our main result is that...

Two-Level Finite Element Discretization of Viscoelastic Fluid Flow

A discontinuous Galerkin finite element discretization of the Euler equations for compressible and incompressible fluids

Using the generalized variable formulation of the Euler equations of fluid dynamics, we develop a numerical method that is capable of simulating the flow of fluids with widely differing thermodynamic behavior: ideal and real gases can be treated with the same method as an incompressible fluid. The well-defined incompressible limit relies on using pressure primitive or entropy variables. In part...

A finite element variational multiscale method for incompressible flow

In this article, we present a finite element variational multiscale (VMS) method for incompressible flows based on two local Gauss integrations, and compare it with common VMS method which is defined by a low order finite element space Lh on the same grid as Xh for the velocity deformation tensor and a stabilization parameter a. The best algorithmic feature of our method is using two local Gaus...

Finite element discretization of a thermoelastic beam

We consider the steady case of a nonlinear model for a thermoelastic beam that can enter in contact with obstacles. We first prove the well-posedness of this problem. Next, we propose a finite element discretization and perform the a priori and a posteriori analysis of the discrete problem. Some numerical experiments confirm the interest of this approach. Résumé: Nous considérons le cas station...