Least-squares spectral element method for three dimensional Stokes equations

•Stokes equations in 3D.•Least squares spectral element method.•Exponential accuracy.•Preconditioner and preconditioned conjugate gradient method.

In this paper we propose a non-conforming least squares spectral element method for Stokes equations on three dimensional domains. Any kind of first order transformation has been avoided by using a block diagonal preconditioner for velocity and pressure variables. Preconditioned conjugate gradient method is used to obtain the numerical solution. The method is proved to be exponentially accurate. Numerical results are provided to validate the proposed estimates.