Two Dimensional Penalty Formulation for Creeping Flow Problems

4 Two Dimensional Penalty Formulation for Creeping Flow Problems 

The isoparametric element works quite well to formulate the finite element equations for flow problems, such as flows with non-Newtonian shear thinning viscosity. Due to the flexibility that exists to integrate variables throughout the elements, the method lends itself 

Algorithm 10 Computing the element stiffness matrix and force vector for a four-noded isoparametric element by numerical integration 

Using the generalized Newtonian constitutive equation, the deviatoric stress tensor is defined as 

The momentum equations can therefore be written in terms of velocities 

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