Mixed Finite Element Galerkin Method Research Articles

Bubble Deformation and Growth Inside Viscoelastic Filaments Undergoing Very Large Extensions

Motivated by the probe experiment for characterizing the adhesion strength of polymeric materials, we studied the axisymmetric extensional flow of a viscoelastic liquid filament that contains one or three initially spherical bubbles along its axis of symmetry. The filament is confined between two parallel and coaxial disks of the same radius and its initially cylindrical outer surface is surrounded by air. The flow is induced by the axial extension of the upper disk under constant velocity, while the lower disk remains stationary. The rheology of the liquid is described by the exponential Phan–Thien and Tanner viscoelastic model. A quasi-elliptic transformation combined with domain decomposition and local mesh refinement is employed to discretize the domain. The mixed finite element Galerkin method for the mass and momentum balances combined with the EVSS-G method and SUPG weighting for the constitutive equation are used to obtain their weak forms. All these are necessary for the successful simulation of ...

Mixed finite element method for a strongly damped wave equation

A mixed finite element Galerkin method is analyzed for a strongly damped wave equation. Optimal error estimates in L2-norm for the velocity and stress are derived using usual energy argument, while those for displacement are based on the nonstandard energy formulation of Baker. Both a semi-discrete scheme and a second-order implicit-time discretization method are discussed, and it is shown that the results are valid for all t > 0. © 2001 John Wiley & Sons, Inc. Numer Methods Partial Differential Eq 17: 105–119, 2001

Mixed finite element method for analysis of viscoelastic fluid flow

In the present paper, numerical analysis of incompressible viscoelastic fluid flow is discussed using mixed finite element Galerkin method. Because Maxwellian viscoelasticity is assumed as the constitutive equation, stress components could not be eliminated from the governing equation system. Because of this, mixed finite element method is utilized to discretize the basic equations. For the solution procedures to solve discretized equation system, Newton-Raphson method for steady flow and perturbation method for unsteady flow is employed. As the numerical examples, comparison was made on the finite element computational results between by direct method and by mixed method. Effects of the viscoelasticity is analyzed for the flows at Reynold's numbers 30, 50 and 70.