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Higher‐order finite volume element methods based on Barlow points for one‐dimensional elliptic and parabolic problems
Author(s) -
Yang Min
Publication year - 2015
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.21924
Subject(s) - mathematics , superconvergence , finite element method , dimension (graph theory) , elliptic partial differential equation , finite volume method for one dimensional steady state diffusion , order (exchange) , partial differential equation , mathematical analysis , parabolic partial differential equation , numerical partial differential equations , pure mathematics , physics , finance , economics , thermodynamics
The article is devoted to a kind of higher‐order finite volume element methods, where the dual partitions are constructed by Barlow points, for elliptic and parabolic problems in one space dimension. Techniques to derive the stability and to control the nonsymmetry are presented. Superconvergence and the optimal order errors in the H 1 ‐ and L 2 ‐norms are obtained. Numerical results illustrate the theoretical findings. © 2014 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 31: 977–994, 2015