Submitted

Superconvergent and Divergence-Free Finite Element Methods for Stokes Equation

Long Chen, Xuehai Huang, Chao Zhang, and Xinyue Zhao

Submitted

arXiv   Bibtex

ABSTRACT:

Superconvergent and divergence-free finite element methods
for the Stokes equation are developed.  The velocity and pressure are
discretized using $H(\mathrm{div})$-conforming vector elements and
discontinuous piecewise polynomials.  The discrete formulation employs
a weak deviatoric gradient operator built with tangential-normal
continuous finite elements for traceless tensors, requiring no
stabilization.  Optimal and superconvergent error estimates are
established.  The method connects to nonconforming virtual element and
pseudostress-velocity-pressure mixed formulations.  Numerical
experiments verify the theory.