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Zbl 1017.76057
Ye, Xiu
On the relationship between finite volume and finite element methods applied to the Stokes equations. (English)
[J] Numer. Methods Partial Differ. Equations 17, No.5, 440-453 (2001). ISSN 0749-159X; ISSN 1098-2426/e

Summary: We investigate a relationship between finite volume and finite element approximations for lower-order elements, both conforming and nonconforming, for 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 convergent finite volume solutions for Stokes equations.

MSC 2000:: *76M12 Finite volume methods
76M10 Finite element methods
76D07 Stokes flows

Keywords: nonconforming elements; conforming elements; finite element method; finite volume method; convergence; lower-order elements; Stokes equations

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Zentralblatt MATH Berlin [Germany]