Complete solutions to extended Stokes' problems.
Conforming finite element approximation of the Stokes problem
Controllability of systems of Stokes equations with one control force : existence of insensitizing controls
Convergence analysis of a locally stabilized collocated finite volume scheme for incompressible flows
We present and analyse in this paper a novel cell-centered collocated finite volume scheme for incompressible flows. Its definition involves a partition of the set of control volumes; each element of this partition is called a cluster and consists in a few neighbouring control volumes. Under a simple geometrical assumption for the clusters, we obtain that the pair of discrete spaces associating the classical cell-centered approximation for the velocities and cluster-wide constant pressures is inf-sup...
Convergence of a finite element discretization of the Navier-Stokes equations in vorticity and stream function formulation
Convergence of a finite element discretization of the Navier-Stokes equations in vorticity and stream function formulation
The standard discretization of the Stokes and Navier–Stokes equations in vorticity and stream function formulation by affine finite elements is known for its bad convergence. We present here a modified discretization, we prove that the convergence is improved and we establish a priori error estimates.
Coupling Darcy and Stokes equations for porous media with cracks
In order to handle the flow of a viscous incompressible fluid in a porous medium with cracks, the thickness of which cannot be neglected, we consider a model which couples the Darcy equations in the medium with the Stokes equations in the cracks by a new boundary condition at the interface, namely the continuity of the pressure. We prove that this model admits a unique solution and propose a mixed formulation of it. Relying on this formulation, we describe a finite element discretization and derive...
Coupling Darcy and Stokes equations for porous media with cracks
In order to handle the flow of a viscous incompressible fluid in a porous medium with cracks, the thickness of which cannot be neglected, we consider a model which couples the Darcy equations in the medium with the Stokes equations in the cracks by a new boundary condition at the interface, namely the continuity of the pressure. We prove that this model admits a unique solution and propose a mixed formulation of it. Relying on this formulation, we describe a finite element discretization and derive...
Coupling of viscous and inviscid Stokes equations via a domain decomposition method for finite elements.
Coupling the Stokes and Navier-Stokes equations with two scalar nonlinear parabolic equations
Coupling the Stokes and Navier–Stokes equations with two scalar nonlinear parabolic equations
This work deals with a system of nonlinear parabolic equations arising in turbulence modelling. The unknowns are the N components of the velocity field u coupled with two scalar quantities θ and φ. The system presents nonlinear turbulent viscosity and nonlinear source terms of the form and lying in L1. Some existence results are shown in this paper, including -estimates and positivity for both θ and φ.
Darcy-type law associated to an optimal control problem.
Decomposition of vector spaces and application to the Stokes problem in arbitrary dimension
Divergence stability in connection with the -version of the finite element method
Domain Decomposition Schemes for the Stokes Equation
Domain Embedding Methods for the Stokes Equations.
Éléments finis mixtes incompressibles pour l'équation de Stokes dans IR3 .
Error estimates for a mixed finite element approximation of the Stokes equations
Error estimates for Stokes problem with Tresca friction conditions
In this paper, we present and study a mixed variational method in order to approximate, with the finite element method, a Stokes problem with Tresca friction boundary conditions. These non-linear boundary conditions arise in the modeling of mold filling process by polymer melt, which can slip on a solid wall. The mixed formulation is based on a dualization of the non-differentiable term which define the slip conditions. Existence and uniqueness of both continuous and discrete solutions of these...