A Least-Squares Spectral Element Formulation for the Stokes Problem

Least-squares spectral element methods seem very promising 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 new element in this work is the choice of spectral elements for the discretization of the least-squares formulation for its superior accuracy due to the high-order basis-functions. The main issue of this paper is the derivation of a least-squares spectral element formulation for the Stokes equations and the role of the boundary conditions on the coercivity relations. The numerical simulations confirm the usual exponential rate of convergence when p-refinement is applied which is typical for spectral element discretization.