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On the relationship between finite volume and finite element methods applied to the Stokes equations
Author(s) -
Ye Xiu
Publication year - 2001
Publication title -
numerical methods for partial differential equations
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.901
H-Index - 61
eISSN - 1098-2426
pISSN - 0749-159X
DOI - 10.1002/num.1021
Subject(s) - mathematics , finite element method , constant (computer programming) , mathematical analysis , bilinear interpolation , convergence (economics) , finite volume method , mixed finite element method , partial differential equation , stokes problem , stokes flow , geometry , mechanics , physics , thermodynamics , statistics , flow (mathematics) , computer science , economics , programming language , economic growth
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.