A new absolutely stable simplified Galerkin Least-Squares finite element method using nonconforming element for the Stokes problem

We propose a new absolutely stable simplified Galerkin Least-Squares (SGLS) finite element method using equal order linear nonconforming element for the Stokes problem. We prove that our method is absolutely stable and has optimal error estimates. Numerical tests confirm and illustrate the theoretical analysis. Compare with the conforming Galerkin Least-Squares method and conforming SGLS method, our nonconforming method is more accuracy.