Submitted

Second order accuracy of a MAC scheme for steady state Stokes equations

Long Chen, Ming Wang and Lin Zhong

Submitted

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ABSTRACT:

 First and second order error estimate on MAC schemes for
solving Stokes equations is obtained in this paper. The scheme
employing quadratic extrapolations to impose boundary conditions is
shown to be second order convergence for velocity and pressure and the
one using linear extrapolation is only first order. In both schemes,
the truncation error at the near boundary nodes are not second order
and the consistency should be measured in a weaker norm. The
stability, i.e, the inf-sup condition, is based on the mixed finite
element formulation of a MAC scheme developed by Han and Wu (SIAM
Numerical Analysis. 35(2), 560--571, 1998).