A Nonconforming Finite Element Method Based On The Orthogonal Polynomials For The Stokes Equation

The Stokes equation is a very important problem in the fluid mechanics, which is studied by many researchers. This article constructs the finite element space based on the orthogonal polynomials. Because of the orthogonality of the polynomials, the proof of the well-posedness becomes relatively simple. Besides, the restrictedness of polynomials at the three edges is also have the orthogonality, which reduces the degrees of the freedom. Then the error estimates are given from which we can see that the construction is able to keep the optimal accuracy of the convergence.