A Global a posteriori Error Estimate for Quasilinear Elliptic Problems.
A heterogeneous alternating-direction method for a micro-macro dilute polymeric fluid model
We examine a heterogeneous alternating-direction method for the approximate solution of the FENE Fokker–Planck equation from polymer fluid dynamics and we use this method to solve a coupled (macro-micro) Navier–Stokes–Fokker–Planck system for dilute polymeric fluids. In this context the Fokker–Planck equation is posed on a high-dimensional domain and is therefore challenging from a computational point of view. The heterogeneous alternating-direction scheme combines a spectral Galerkin method for...
A hybrid multigrid method for the steady-state incompressible Navier-Stokes equations.
A logarithmic regularity criterion for 3D Navier-Stokes system in a bounded domain
This paper proves a logarithmic regularity criterion for 3D Navier-Stokes system in a bounded domain with the Navier-type boundary condition.
A lower bound for the principal eigenvalue of the Stokes operator in a random domain
This article is dedicated to localization of the principal eigenvalue (PE) of the Stokes operator acting on solenoidal vector fields that vanish outside a large random domain modeling the pore space in a cubic block of porous material with disordered micro-structure. Its main result is an asymptotically deterministic lower bound for the PE of the sum of a low compressibility approximation to the Stokes operator and a small scaled random potential term, which is applied to produce a similar bound...
A mathematical model for core-annular fluids with surfactants.
A mathematical model for resin transfer molding
A Mixed Finite Element Approximation of the Navier-Stokes Equations.
A Mixed Finite Element Method for Solving the Nonstationary Stokes Equation.
A mixed finite element method for the Navier-Stokes equations
A mixed formulation of a sharp interface model of stokes flow with moving contact lines
Two-phase fluid flows on substrates (i.e. wetting phenomena) are important in many industrial processes, such as micro-fluidics and coating flows. These flows include additional physical effects that occur near moving (three-phase) contact lines. We present a new 2-D variational (saddle-point) formulation of a Stokesian fluid with surface tension that interacts with a rigid substrate. The model is derived by an Onsager type principle using shape differential calculus (at the sharp-interface, front-tracking...
A model for dip-coating of a two liquid mixture.
A modified Cayley transform for the discretized Navier-Stokes equations
This paper is concerned with the problem of computing a small number of eigenvalues of large sparse generalized eigenvalue problems. The matrices arise from mixed finite element discretizations of time dependent equations modelling viscous incompressible flow. The eigenvalues of importance are those with smallest real part and are used to determine the linearized stability of steady states, and could be used in a scheme to detect Hopf bifurcations. We introduce a modified Cayley transform of the...
A modified streamline diffusion method for solving the stationary Navier-Stokes equation.
A multidomain spectral collocation method for the Stokes problem.
A multigrid method for a Petrov-Galerkin discretization of the Stokes equations.
A multilayer Saint-Venant system with mass exchanges for shallow water flows. Derivation and numerical validation
The standard multilayer Saint-Venant system consists in introducing fluid layers that are advected by the interfacial velocities. As a consequence there is no mass exchanges between these layers and each layer is described by its height and its average velocity. Here we introduce another multilayer system with mass exchanges between the neighboring layers where the unknowns are a total height of water and an average velocity per layer. We derive it from Navier-Stokes system with an hydrostatic pressure...
A multilayer Saint-Venant system with mass exchanges for shallow water flows. Derivation and numerical validation*
The standard multilayer Saint-Venant system consists in introducing fluid layers that are advected by the interfacial velocities. As a consequence there is no mass exchanges between these layers and each layer is described by its height and its average velocity. Here we introduce another multilayer system with mass exchanges between the neighboring layers where the unknowns are a total height of water and an average velocity per layer. We derive it from Navier-Stokes system with an hydrostatic...
A multilevel method of nonlinear Galerkin type for the Navier-Stokes equations.
A new approach to the -regularity theorems for linear stationary nonhomogeneous Stokes systems.