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Center for Nonlinear Studies |
In the last ten to twenty years a very large number of publications has appeared proposing finite element methods for flow calculations. The methods are generally known as stabilization schemes and include the Petrov-Galerkin, SUPG, Galerkin-Least-Squares, discontinuous Galerkin and others. Unfortunately the abundance of names and literature can make it very confusing and time consuming for potential users to understand the rational behind the algorithms as well as their differences, advantages and disadvantages. The basic ideas behind the various stabilization schemes are presented at the basic level, and extended to their application in the solution of the Navier-Stokes equations. The consistency of finite element formulations is also discussed, and the use of finite element algorithms in coupled physics problems is illustrated through examples involving flow, heat and mass transfer and interface interactions and evolutions.