Fourier analysis of stabilized Q(1)-Q(1) mixed finite element approximation

摘要

We use Fourier analysis to investigate the instability of an equal-order mixed finite element approximation method for elliptic incompressible ow equations. The lack of stability can be attributed to the fact that the associated discrete Ladyzhenskaya-Babuska-Brezzi (LBB) constant tends to zero as the mesh size is reduced. We develop a stabilization approach that is appropriate to the periodic setting and deduce optimal choices of the associated stabilization parameter. [References: 13]