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L p error estimates and superconvergence for covolume or finite volume element methods
Author(s) -
Chou SoHsiang,
Kwak Do Y.,
Li Qian
Publication year - 2003
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.10059
Subject(s) - superconvergence , mathematics , finite element method , norm (philosophy) , partial differential equation , duality (order theory) , finite volume method , convergence (economics) , mathematical analysis , pure mathematics , thermodynamics , physics , political science , law , economics , economic growth
We consider convergence of the covolume or finite volume element solution to linear elliptic and parabolic problems. Error estimates and superconvergence results in the L p norm, 2 ≤ p ≤ ∞, are derived. We also show second‐order convergence in the L p norm between the covolume and the corresponding finite element solutions and between their gradients. The main tools used in this article are an extension of the “supercloseness” results in Chou and Li [Math Comp 69(229) (2000), 103–120] to the L p based spaces, duality arguments, and the discrete Green's function method. © 2003 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 19: 463–486, 2003