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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

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 Ω ⊂ ℝd, d = 2 or 3, for the velocity...

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

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 ,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 equation....

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

John W. Barrett, Endre Süli (2011)

ESAIM: Mathematical Modelling and Numerical Analysis

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 , 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 equation....

Finite element approximations of a glaciology problem

Sum S. Chow, Graham F. Carey, Michael L. Anderson (2004)

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

In this paper we study a model problem describing the movement of a glacier under Glen’s flow law and investigated by Colinge and Rappaz [Colinge and Rappaz, ESAIM: M2AN 33 (1999) 395–406]. We establish error estimates for finite element approximation using the results of Chow [Chow, SIAM J. Numer. Analysis 29 (1992) 769–780] and Liu and Barrett [Liu and Barrett, SIAM J. Numer. Analysis 33 (1996) 98–106] and give an analysis of the convergence of the successive approximations used in [Colinge and...

Finite element approximations of a glaciology problem

Sum S. Chow, Graham F. Carey, Michael L. Anderson (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

In this paper we study a model problem describing the movement of a glacier under Glen's flow law and investigated by Colinge and Rappaz [Colinge and Rappaz, ESAIM: M2AN33 (1999) 395–406]. We establish error estimates for finite element approximation using the results of Chow [Chow, SIAM J. Numer. Analysis29 (1992) 769–780] and Liu and Barrett [Liu and Barrett, SIAM J. Numer. Analysis33 (1996) 98–106] and give an analysis of the convergence of the successive approximations used in [Colinge and...

Finite element approximations of the three dimensional Monge-Ampère equation

Susanne Cecelia Brenner, Michael Neilan (2012)

ESAIM: Mathematical Modelling and Numerical Analysis

In this paper, we construct and analyze finite element methods for the three dimensional Monge-Ampère equation. We derive methods using the Lagrange finite element space such that the resulting discrete linearizations are symmetric and stable. With this in hand, we then prove the well-posedness of the method, as well as derive quasi-optimal error estimates. We also present some numerical experiments that back up the theoretical findings.

Finite element approximations of the three dimensional Monge-Ampère equation

Susanne Cecelia Brenner, Michael Neilan (2012)

ESAIM: Mathematical Modelling and Numerical Analysis

In this paper, we construct and analyze finite element methods for the three dimensional Monge-Ampère equation. We derive methods using the Lagrange finite element space such that the resulting discrete linearizations are symmetric and stable. With this in hand, we then prove the well-posedness of the method, as well as derive quasi-optimal error estimates. We also present some numerical experiments that back up the theoretical findings.

Finite element derivative interpolation recovery technique and superconvergence

Tie Zhu Zhang, Shu Hua Zhang (2011)

Applications of Mathematics

A new finite element derivative recovery technique is proposed by using the polynomial interpolation method. We show that the recovered derivatives possess superconvergence on the recovery domain and ultraconvergence at the interior mesh points for finite element approximations to elliptic boundary problems. Compared with the well-known Z-Z patch recovery technique, the advantage of our method is that it gives an explicit recovery formula and possesses the ultraconvergence for the odd-order finite...

Finite element discretization of Darcy's equations with pressure dependent porosity

Vivette Girault, François Murat, Abner Salgado (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

We consider the flow of a viscous incompressible fluid through a rigid homogeneous porous medium. The permeability of the medium depends on the pressure, so that the model is nonlinear. We propose a finite element discretization of this problem and, in the case where the dependence on the pressure is bounded from above and below, we prove its convergence to the solution and propose an algorithm to solve the discrete system. In the case where the dependence on the pressure is exponential, we propose...

Currently displaying 81 – 100 of 372