Application of Least-Squares Spectral Element Methods to Incompressible Flow Problems

Abstract

Least-squares spectral element methods are based on two important and successful numerical methods: spectral /hp element methods and least-squares finite element methods. In this respect, least-squares spectral element methods are very powerfull since they combine the generality of finite element methods with the accuracy of the spectral methods and also the theoretical and computational advantages in the algorithmic design and implementation of the least-squares methods. The present paper continues the development of the least-squares spectral element methods by concentrating on the application of this method to incompressible flow problems. Therefore, the derivation of the least-squares spectral element formulation of the velocity-vorticity-pressure form of the unsteady Navier-Stokes equations plays a central role in the present paper. Moreover, the numerical simulation of the lid driven cavity problem confirms that the least-squares spectral element method produces spectrally accurate results.