Galerkin finite element models

Detailed derivations of the least-squares and Galerkin finite element models of the laminar suspension flows are given elsewhere [10,11] only brief outlines will be presented here. 

This paper will discuss the formulation of the simulator for the filament winding process which describes the temperature and extent of cure in a cross-section of a composite part. The model consists of two parts the kinetic model to predict the curing kinetics of the polymeric system and the heat transfer model which incorporates the kinetic model. A Galerkin finite element code was written to solve the specially and time dependent system. The program was implemented on a microcomputer to minimize computer costs. 

In order to solve viscoelastic problems, we must select the most convenient model for the stress and then proceed to develop the finite element formulation. Doue to the excess in non-linearity and coupling of the viscoelastic momentum equations, three distinct Galerkin formulations are used for the governing equations, i.e., we use different shape functions for the viscoelastic stress, the velocity and the pressure... 

J. Baranger and D. Sandri, Some remarks on the discontinuous Galerkin method for the finite element approximation of the Oldroyd-B model, submitted. 

This paper describes a finite element formulation designed to simulate polymer melt flows in which both conductive and convective heat transfer may be important, and illustrates the numerical model by means of computer experiments using Newtonian extruder drag flow and entry flow as trial problems. Fluid incompressibility is enforced by a penalty treatment of the element pressures, and the thermal convective transport is modeled by conventional Galerkin and optimal upwind treatments. 

The prediction horizon is discretized in cycles, where a cycle is a switching time tshift multiplied by the total number of columns. Equation 9.1 constitutes a dynamic optimization problem with the transient behavior of the process as a constraint f describes the continuous dynamics of the columns based on the general rate model (GRM) as well as the discrete switching from period to period. To solve the PDE models of columns, a Galerkin method on finite elements is used for the liquid... 

For the solution of the PDE models of the columns, a Galerkin method on finite elements is used for the liquid phase and orthogonal collocation for the solid phase. The switching of the node equations is considered explicitly, that is, a full hybrid plant model is used. The objective function F is the sum of the costs incurred for each cycle (e.g., the desorbent consumption) and a regularizing term that is added in order to smooth the input sequence in order to avoid high fluctuations of the inputs from cycle to cyde. The first equality constraint represents the plant model... 

The near-field region is modeled by conventional finite elements (Zienkiewicz et al. 1999). Discretized equations of motion can be obtained using the Galerkin method. 

A. Onorati, M. Perotti, and S. Rebay. Modelling one-dimensional unsteady flows in ducts Symmetric finite difference schemes versus galerkin discontinuous finite element methods. International Journal of Mechanical Sciences, 39(11) 1213-1236, 1997. 

Stephens MM, Moorhead ED (1987) A global finite element Galerkin/B-spline (GBS) numerical model of electrochemical kinetics, transport and mechanism for multi-geometry working electrodes. Part 1. Modeled Nernstian voltammetry. J Electroanal Chem 220 1. 

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