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On the relationship between finite volume and finite element methods applied to the Stokes equations. (English) Zbl 1017.76057
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:
76M12Finite volume methods (fluid mechanics)
76M10Finite element methods (fluid mechanics)
76D07Stokes and related (Oseen, etc.) flows