Displaying similar documents to “Finite element approximation of finitely extensible nonlinear elastic dumbbell models for dilute polymers”

Finite element approximation of finitely extensible nonlinear elastic dumbbell models for dilute polymers

John W. Barrett, Endre Süli (2012)

ESAIM: Mathematical Modelling and Numerical Analysis

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We construct a Galerkin finite element method for the numerical approximation of weak solutions to a general class of coupled FENE-type finitely extensible nonlinear elastic dumbbell models that arise from the kinetic theory of dilute solutions of polymeric liquids with noninteracting polymer chains. The class of models involves the unsteady incompressible Navier–Stokes equations in a bounded domain  ⊂ ℝ,  = 2 or 3, for ...

Finite element approximation of kinetic dilute polymer models with microscopic cut-off

John W. Barrett, Endre Süli (2011)

ESAIM: Mathematical Modelling and Numerical Analysis

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We construct a Galerkin finite element method for the numerical approximation of weak solutions to a coupled microscopic-macroscopic bead-spring model that arises from the kinetic theory of dilute solutions of polymeric liquids with noninteracting polymer chains. The model consists of the unsteady incompressible Navier–Stokes equations in a bounded domain Ω ⊂ ℝ d , = 2 or 3, for the velocity and the pressure of the fluid, with an elastic extra-stress tensor as right-hand side in the momentum...

Finite element approximation of kinetic dilute polymer models with microscopic cut-off

John W. Barrett, Endre Süli (2011)

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

Similarity:

We construct a Galerkin finite element method for the numerical approximation of weak solutions to a coupled microscopic-macroscopic bead-spring model that arises from the kinetic theory of dilute solutions of polymeric liquids with noninteracting polymer chains. The model consists of the unsteady incompressible Navier–Stokes equations in a bounded domain Ω ⊂ ℝ d ,= 2 or 3, for the velocity and the pressure of the fluid, with an elastic extra-stress tensor as right-hand side in the momentum...

Stabilization methods of bubble type for the -element applied to the incompressible Navier-Stokes equations

Petr Knobloch, Lutz Tobiska (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

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In this paper, a general technique is developed to enlarge the velocity space V h 1 of the unstable -element by adding spaces V h 2 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 -element and the 4-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...

On the two-dimensional compressible isentropic Navier–Stokes equations

Catherine Giacomoni, Pierre Orenga (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

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We analyze the compressible isentropic Navier–Stokes equations (Lions, 1998) in the two-dimensional case with γ = c p / c v = 2 . These equations also modelize the shallow water problem in height-flow rate formulation used to solve the flow in lakes and perfectly well-mixed sea. We establish a convergence result for the time-discretized problem when the momentum equation and the continuity equation are solved with the Galerkin method, without adding a penalization term in the continuity equation as...