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

We investigate the relationship between finite volume and finite element ap proximations for the lower-order elements, both conforming and nonconformin g for the Stokes equations. These elements include conforming, linear veloc ity-constant pressure on triangles, conforming bilinear velocity-constant p ressure on rectangles and their macro-element versions, and nonconforming l inear velocity-constant pressure on triangles and nonconforming rotated bil inear velocity-constant pressure on rectangles. By applying the relationshi p between the two methods, we obtain the convergence finite volume solution s for the Stokes equations. (C) 2001 John Wiley & Sons, Inc.