Separation of variables in the Stokes problem application to its finite element multiscale approximation
Simulation of incompressible flows with heat and mass transfer using parallel finite element method.
Solution of Stefan problems by fully discrete linear schemes.
Some New Families of Finite Elements for the Stokes Equations.
Spectral-finite element method for compressible fluid flows
Stability of a finite element method for 3D exterior stationary Navier-Stokes flows
We consider numerical approximations of stationary incompressible Navier-Stokes flows in 3D exterior domains, with nonzero velocity at infinity. It is shown that a P1-P1 stabilized finite element method proposed by C. Rebollo: A term by term stabilization algorithm for finite element solution of incompressible flow problems, Numer. Math. 79 (1998), 283–319, is stable when applied to a Navier-Stokes flow in a truncated exterior domain with a pointwise boundary condition on the artificial boundary....
Stabilization methods of bubble type for the -element applied to the incompressible Navier-Stokes equations
Stabilization methods of bubble type for the Q1/Q1-element applied to the incompressible Navier-Stokes equations
In this paper, a general technique is developed to enlarge the velocity space of the unstable -element by adding spaces such that for the extended pair the Babuska-Brezzi condition is satisfied. Examples of stable elements which can be derived in such a way imply the stability of the well-known Q2/Q1-element and the 4Q1/Q1-element. However, our new elements are much more cheaper. In particular, we shall see that more than half of the additional degrees of freedom when switching from the Q1...
Stabilization of a non standard FETI-DP mortar method for the Stokes problem
In a recent paper [E. Chacón Vera and D. Franco Coronil, J. Numer. Math. 20 (2012) 161–182.] a non standard mortar method for incompressible Stokes problem was introduced where the use of the trace spaces H1 / 2and H1/200and a direct computation of the pairing of the trace spaces with their duals are the main ingredients. The importance of the reduction of the number of degrees of freedom leads naturally to consider the stabilized version and this is the results we present in this work. We prove...
Stabilized finite element methods for miscible displacement in porous media
Stabilized Galerkin finite element methods for convection dominated and incompressible flow problems
In this paper, we analyze a class of stabilized finite element formulations used in computation of (i) second order elliptic boundary value problems (diffusion-convection-reaction model) and (ii) the Navier-Stokes problem (incompressible flow model). These stabilization techniques prevent numerical instabilities that might be generated by dominant convection/reaction terms in (i), (ii) or by inappropriate combinations of velocity/pressure interpolation functions in (ii). Stability and convergence...
Stabilized Galerkin methods for magnetic advection
Taking the cue from stabilized Galerkin methods for scalar advection problems, we adapt the technique to boundary value problems modeling the advection of magnetic fields. We provide rigorous a priori error estimates for both fully discontinuous piecewise polynomial trial functions and -conforming finite elements.
Staggered schemes for all speed flows
We review in this paper a class of schemes for the numerical simulation of compressible flows. In order to ensure the stability of the discretizations in a wide range of Mach numbers and introduce sufficient decoupling for the numerical resolution, we choose to implement and study pressure correction schemes on staggered meshes. The implicit version of the schemes is also considered for the theoretical study. We give both algorithms for the barotropic Navier-Stokes equations, for the full Navier-Stokes...
Steady compressible Oseen flow with slip boundary conditions
We prove the existence of solution in the class H²(Ω) × H¹(Ω) to the steady compressible Oseen system with slip boundary conditions in a two dimensional, convex domain with boundary of class . The method is to regularize a weak solution obtained via the Galerkin method. The problem of regularization is reduced to the problem of solvability of a certain transport equation by application of the Helmholtz decomposition. The method works under an additional assumption on the geometry of the boundary....
Stick-slip transition capturing by using an adaptive finite element method
The numerical modeling of the fully developed Poiseuille flow of a newtonian fluid in a square section with slip yield boundary condition at the wall is presented. The stick regions in outer corners and the slip region in the center of the pipe faces are exhibited. Numerical computations cover the complete range of the dimensionless number describing the slip yield effect, from a full slip to a full stick flow regime. The resolution of variational inequalities describing the flow is based on the...
Stick-slip transition capturing by using an adaptive finite element method
The numerical modeling of the fully developed Poiseuille flow of a Newtonian fluid in a square section with slip yield boundary condition at the wall is presented. The stick regions in outer corners and the slip region in the center of the pipe faces are exhibited. Numerical computations cover the complete range of the dimensionless number describing the slip yield effect, from a full slip to a full stick flow regime. The resolution of variational inequalities describing the flow is based on the...
Streamline diffusion methods for the Vlasov-Poisson equation
Sur l'approximation numérique des écoulements quasi-newtoniens dont la viscosité suit la loi puissance ou la loi de Carreau
Sur un algorithme en volumes finis non structurés pour la simulation des flammes turbulentes en chimie infiniment rapide