Submitted

Some First and Second Order Finite Volume Methods for the Stokes Problem

Long Chen

Submitted

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ABSTRACT:

A new Taylor-Hood type finite volume method for the Stokes equations
is developed by a simple modification from the corresponding finite
element methods. The conservation of momentum is preserved locally
over each control volume on the dual mesh and the conservation of mass
is over each cell on the primary mesh. Optimal second order
convergence is obtained under a mild constrain on the
triangulations. Note that this is the first second order finite volume
method for the Stokes equations. Two first order finite volume methods
are also developed and analyzed.