Performance of nonconforming spectral element method for Stokes problems

TL;DR

This paper evaluates a non-conforming spectral element method for solving Stokes problems, demonstrating exponential accuracy and efficiency across various complex test cases.

Contribution

It introduces a high-order non-conforming spectral element approach for Stokes problems, showing exponential accuracy and effective solution techniques.

Findings

Exponential accuracy achieved for generalized Stokes problems.

Efficient solution via preconditioned conjugate gradient method.

Successful application to complex domains and boundary conditions.

Abstract

In this paper, we study the performance of the non-conforming least-squares spectral element method for Stokes problem. Generalized Stokes problem has been considered and the method is shown to be exponential accurate. The numerical method is nonconforming and higher order spectral element functions are used. The same order spectral element functions are used for both velocity and pressure variables. The normal equations in the least-squares formulation are solved efficiently using preconditioned conjugate gradient method. Various test cases are considered including the Stokes problem on curvilinear domains, Stokes problem with mixed boundary conditions and a generalized stokes problem in \mathbb{R}^{3} to verify the accuracy of the method.