Displaying similar documents to “Finite element analysis of a simplified stochastic Hookean dumbbells model arising from viscoelastic flows”

Existence, a priori and a posteriori error estimates for a nonlinear three-field problem arising from Oldroyd-B viscoelastic flows

Marco Picasso, Jacques Rappaz (2001)

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

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In this paper, a nonlinear problem corresponding to a simplified Oldroyd-B model without convective terms is considered. Assuming the domain to be a convex polygon, existence of a solution is proved for small relaxation times. Continuous piecewise linear finite elements together with a Galerkin Least Square (GLS) method are studied for solving this problem. Existence and a priori error estimates are established using a Newton-chord fixed point theorem, a posteriori error estimates are...

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

Vivette Girault, François Murat, Abner Salgado (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

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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,...

The Mortar finite element method for Bingham fluids

Patrick Hild (2001)

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

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This paper deals with the flow problem of a viscous plastic fluid in a cylindrical pipe. In order to approximate this problem governed by a variational inequality, we apply the nonconforming mortar finite element method. By using appropriate techniques, we are able to prove the convergence of the method and to obtain the same convergence rate as in the conforming case.

Stabilized Galerkin finite element methods for convection dominated and incompressible flow problems

Gert Lube (1994)

Banach Center Publications

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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...

Optimal convergence and a posteriori error analysis of the original DG method for advection-reaction equations

Tie Zhu Zhang, Shu Hua Zhang (2015)

Applications of Mathematics

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We consider the original DG method for solving the advection-reaction equations with arbitrary velocity in d space dimensions. For triangulations satisfying the flow condition, we first prove that the optimal convergence rate is of order k + 1 in the L 2 -norm if the method uses polynomials of order k . Then, a very simple derivative recovery formula is given to produce an approximation to the derivative in the flow direction which superconverges with order k + 1 . Further we consider a residual-based...

Finite-element discretizations of a two-dimensional grade-two fluid model

Vivette Girault, Larkin Ridgway Scott (2001)

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

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We propose and analyze several finite-element schemes for solving a grade-two fluid model, with a tangential boundary condition, in a two-dimensional polygon. The exact problem is split into a generalized Stokes problem and a transport equation, in such a way that it always has a solution without restriction on the shape of the domain and on the size of the data. The first scheme uses divergence-free discrete velocities and a centered discretization of the transport term, whereas the...