Stokes Equations and Penalty Method
In this chapter, we will introduce the penalty finite element formulation for both Newtonian and power-law non-Newtonian Stokes flows. The penalty finite element method has been recognized as one of the most effective numerical methods in solving fluid flow problems by many in academics as well as in industry (see, e.g., Fastook 1993 and Fidap 1999). We will derive local finite element matrices by using the linear triangular and the bilinear rectangular elements. We will use the method of steepest descent, the conjugate gradient methods for the linear Stokes problem, and nonlinear conjugate gradient methods for the nonlinear Stokes problem. The cavity problem will be used as an example of numerical implementation.
KeywordsConjugate Gradient Method Penalty Method Stoke Flow Finite Element Solution Connectivity Matrix
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