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Analysis and convergence of finite volume method using discontinuous bilinear functions
Author(s) -
Ye Xiu
Publication year - 2008
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.20266
Subject(s) - mathematics , bilinear interpolation , finite volume method , norm (philosophy) , convergence (economics) , bilinear form , partial differential equation , partial derivative , mathematical analysis , finite volume method for one dimensional steady state diffusion , error analysis , order (exchange) , numerical partial differential equations , mechanics , statistics , physics , political science , law , economics , economic growth , finance
We develop finite volume method using discontinuous bilinear functions on rectangular mesh. This method is analyzed for the Stokes equations. An optimal error estimate for the approximation of velocity is obtained in a mesh‐dependent norm. First order L 2 ‐error estimates are derived for the approximations of both velocity and pressure. © 2007 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2007