Superconvergence of Mixed Finite Element Method with Bernstein Polynomials for Stokes Problem

Abstract

In this paper, we employ interpolation and projection methodologies to establish a superconvergence outcome for the Stokes problem, as approximated by the mixed finite element method (FEM) utilizing Bernstein polynomial basis functions. It is widely recognized that the convergence rate of the FEM in the L2-norm is O(hm+2). However, this paper presents an innovative superconvergence result: specifically, in terms of the L2-norm, the error convergence rate between the mixed finite element approximate solution and the local projection is O(hm+2), with m denoting the order of the Bernstein polynomial basis function.

Keywords

• superconvergence
• mixed finite element method
• Stokes problem
• error estimate
• Bernstein polynomials