On the relationship between finite volume and finite element methods applied to the Stokes equations

Abstract

We investigate the relationship between finite volume and finite element approximations for the lower-order elements, both conforming and nonconforming for the Stokes equations. These elements include conforming, linear velocity-constant pressure on triangles, conforming bilinear velocity-constant pressure on rectangles and their macro-element versions, and nonconforming linear velocity-constant pressure on triangles and nonconforming rotated bilinear velocity-constant pressure on rectangles. By applying the relationship between the two methods, we obtain the convergence finite volume solutions for the Stokes equations. © 2001 John Wiley & Sons, Inc.