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Error estimates for two‐level penalty finite volume method for the stationary Navier–Stokes equations
Author(s) -
Huang Pengzhan,
Feng Xinlong
Publication year - 2013
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.2736
Subject(s) - mathematics , penalty method , finite element method , navier–stokes equations , finite volume method , convergence (economics) , rate of convergence , stokes flow , mathematical analysis , mathematical optimization , geometry , mechanics , compressibility , computer science , physics , flow (mathematics) , key (lock) , computer security , economics , thermodynamics , economic growth
Two‐level penalty finite volume method for the stationary Navier–Stokes equations based on the P 1 − P 0 element is considered in this paper. The method involves solving one small penalty Navier–Stokes problem on a coarse mesh with mesh size H = ϵ 1 / 4 h 1 / 2 , a large penalty Stokes problem on a fine mesh with mesh size h , where 0 < ϵ < 1 is a penalty parameter. The method we study provides an approximate solutionu ϵ h , p ϵ hwith the convergence rate of same order as the penalty finite volume solution ( u ϵh , p ϵh ), which involves solving one large penalty Navier–Stokes problem on a fine mesh with the same mesh size h . However, our method can save a large amount of computational time. Copyright © 2013 John Wiley & Sons, Ltd.