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

✍ Scribed by Xiu Ye

• Publisher: John Wiley and Sons
• Year: 2001
• Tongue: English
• Weight: 138 KB
• Volume: 17
• Category: Article
• ISSN: 0749-159X
• DOI: 10.1002/num.1021

✦ Synopsis

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. Numer Methods Partial Differential Eq 17: 440–453, 2001.