More pressure in the finite element discretization of the Stokes problem
More pressure in the finite element discretization of the Stokes problem
For the Stokes problem in a two- or three-dimensional bounded domain, we propose a new mixed finite element discretization which relies on a nonconforming approximation of the velocity and a more accurate approximation of the pressure. We prove that the velocity and pressure discrete spaces are compatible, in the sense that they satisfy an inf-sup condition of Babuška and Brezzi type, and we derive some error estimates.
Mortar finite element discretization of a model coupling Darcy and Stokes equations
As a first draft of a model for a river flowing on a homogeneous porous ground, we consider a system where the Darcy and Stokes equations are coupled via appropriate matching conditions on the interface. We propose a discretization of this problem which combines the mortar method with standard finite elements, in order to handle separately the flow inside and outside the porous medium. We prove a priori and a posteriori error estimates for the resulting discrete problem. Some numerical experiments...
Multimodels for incompressible flows : iterative solutions for the Navier-Stokes / Oseen coupling
In a recent paper [4] we have proposed and analysed a suitable mathematical model which describes the coupling of the Navier-Stokes with the Oseen equations. In this paper we propose a numerical solution of the coupled problem by subdomain splitting. After a preliminary analysis, we prove a convergence result for an iterative algorithm that alternates the solution of the Navier-Stokes problem to the one of the Oseen problem.
Multimodels for incompressible flows: iterative solutions for the Navier-Stokes/Oseen coupling
In a recent paper [4] we have proposed and analysed a suitable mathematical model which describes the coupling of the Navier-Stokes with the Oseen equations. In this paper we propose a numerical solution of the coupled problem by subdomain splitting. After a preliminary analysis, we prove a convergence result for an iterative algorithm that alternates the solution of the Navier-Stokes problem to the one of the Oseen problem.
Multi-parameter asymptotic error resolution of the mixed finite element method for the Stokes problem
Multi-parameter asymptotic error resolution of the mixed finite element method for the Stokes problem
In this paper, a multi-parameter error resolution technique is applied into a mixed finite element method for the Stokes problem. By using this technique and establishing a multi-parameter asymptotic error expansion for the mixed finite element method, an approximation of higher accuracy is obtained by multi-processor computers in parallel.
Navier-Stokes/Darcy coupling: modeling, analysis, and numerical approximation.
New wall laws for the unsteady incompressible Navier-Stokes equations on rough domains
Different effective boundary conditions or wall laws for unsteady incompressible Navier-Stokes equations over rough domains are derived in the laminar setting. First and second order unsteady wall laws are proposed using two scale asymptotic expansion techniques. The roughness elements are supposed to be periodic and the influence of the rough boundary is incorporated through constitutive constants. These constants are obtained by solving steady Stokes problems and so they are calculated only once....
New Wall Laws for the Unsteady Incompressible Navier-Stokes Equations on Rough Domains
Different effective boundary conditions or wall laws for unsteady incompressible Navier-Stokes equations over rough domains are derived in the laminar setting. First and second order unsteady wall laws are proposed using two scale asymptotic expansion techniques. The roughness elements are supposed to be periodic and the influence of the rough boundary is incorporated through constitutive constants. These constants are obtained by solving steady Stokes problems and so they are calculated only...
Non-matching mortar discretization analysis for the coupling Stokes-Darcy equations.
Numerical algorithm for the stationary, nonhomogeneous Navier-Stokes equations.
Numerical analysis of Euler-SUPG modified method for transient viscoelastic flow.
Numerical analysis of the Navier-Stokes equations
This paper discusses some conceptional questions of the numerical simulation of viscous incompressible flow which are related to the presence of boundaries.
Numerical approximation of nematic liquid crystal flows governed by the Ericksen-Leslie equations
Numerical approximation of the flow of liquid crystals governed by the Ericksen-Leslie equations is considered. Care is taken to develop numerical schemes which inherit the Hamiltonian structure of these equations and associated stability properties. For a large class of material parameters compactness of the discrete solutions is established which guarantees convergence.
Numerical approximation of nematic liquid crystal flows governed by the Ericksen-Leslie equations*
Numerical approximation of the flow of liquid crystals governed by the Ericksen-Leslie equations is considered. Care is taken to develop numerical schemes which inherit the Hamiltonian structure of these equations and associated stability properties. For a large class of material parameters compactness of the discrete solutions is established which guarantees convergence.
Numerical approximations of the relative rearrangement : the piecewise linear case. Application to some nonlocal problems
Numerical Approximations of the Relative Rearrangement: The piecewise linear case. Application to some Nonlocal Problems
We first prove an abstract result for a class of nonlocal problems using fixed point method. We apply this result to equations revelant from plasma physic problems. These equations contain terms like monotone or relative rearrangement of functions. So, we start the approximation study by using finite element to discretize this nonstandard quantities. We end the paper by giving a numerical resolution of a model containing those terms.
Numerical homogenization of well singularities in the flow transport through heterogeneous porous media: fully discrete scheme
Motivated by well-driven flow transport in porous media, Chen and Yue proposed a numerical homogenization method for Green function [Multiscale Model. Simul.1 (2003) 260–303]. In that paper, the authors focused on the well pore pressure, so the local error analysis in maximum norm was presented. As a continuation, we will consider a fully discrete scheme and its multiscale error analysis on the velocity field.
Numerical methods for fourth order nonlinear degenerate diffusion problems
Numerical schemes are presented for a class of fourth order diffusion problems. These problems arise in lubrication theory for thin films of viscous fluids on surfaces. The equations being in general fourth order degenerate parabolic, additional singular terms of second order may occur to model effects of gravity, molecular interactions or thermocapillarity. Furthermore, we incorporate nonlinear surface tension terms. Finally, in the case of a thin film flow driven by a surface active agent (surfactant),...