Convergence of a linearly extrapolated BDF2 finite element scheme for viscoelastic fluid flow

Convergence of a linearly extrapolated BDF2 finite element scheme for viscoelastic fluid flow

The stability and convergence of a linearly extrapolated second order backward difference (BDF2-LE) time-stepping scheme for solving viscoelastic fluid flow in Rd , d = 2, 3, are presented in this paper. The time discretization is based on the implicit scheme for the linear term and the two-step linearly extrapolated scheme for the nonlinear term. Mixed finite element (MFE) method is applied fo...

Two-Level Finite Element Discretization of Viscoelastic Fluid Flow

Simulation for Viscoelastic Flow by a Finite Volume/Element Method

Stability of a second-order finite element/finite volume hybrid scheme is investigated on the basis of flows with increasing Weissenberg number. Finite elements are used to discretise the balances of mass and momentum. For the stress equation a finite volume method is used, based on the recent development with fluctuation distribution schemes for pure convection problems. Examples considered in...

Mixed finite element methods for viscoelastic flow analysis: A review

The progress made during the past decade in the application of mixed finite element methods to solve viscoelastic flow problems using differential constitutive equations is reviewed. The algorithmic developments are discussed in detail. Starting with the classical mixed formulation, the elastic viscous stress splitting (EVSS) method as well as the related discrete EVSS and the so-called EVSS-G ...

Analysis and finite element approximation of an optimal control problem for the Oseen viscoelastic fluid flow

In this article we study a boundary control problem for an Oseen-type model of viscoelastic fluid flow. The existence of a unique optimal solution is proved and an optimality system is derived by the first-order necessary condition. We investigate finite element approximations to a solution of the optimality system, and a solution algorithm for the system based on the gradient method. © 2007 El...