A stabilized finite element method for the incompressible Navier–Stokes equations using a hierarchical basis

Stabilized finite element methods have been shown to yield robust, accurate numerical solutions to both the compressible and incompressible Navier-Stokes equations for laminar and turbulent flows. The present work focuses on the application of higher-order, hierarchical basis functions to the incompressible Navier-Stokes equations using a stabilized finite element method. It is shown on a variety of problems that the most cost-effective simulations (in terms of CPU time, memory, and disk storage) can be obtained using higher-order basis functions when compared with the traditional linear basis. In addition, algorithms will be presented for the efficient implementation of these methods within the traditional finite element data structures

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