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

TLDR

Stabilized finite element methods provide robust, accurate solutions for both compressible and incompressible Navier–Stokes equations in laminar and turbulent flows. This study applies higher‑order hierarchical basis functions to the incompressible Navier–Stokes equations using a stabilized finite element method. The authors present algorithms for efficiently implementing these higher‑order methods within conventional finite element data structures. Across various test cases, higher‑order basis functions yield the most cost‑effective simulations in terms of CPU time, memory, and disk storage compared to traditional linear bases. © 2001 John Wiley & Sons, Ltd.

Abstract

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. Copyright © 2001 John Wiley & Sons, Ltd.