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The local ultraconvergence of high‐order finite element method for second‐order elliptic problems with constant coefficients over a rectangular partition
Author(s) -
He Wenming
Publication year - 2019
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.22398
Subject(s) - mathematics , finite element method , extrapolation , partition (number theory) , constant (computer programming) , mathematical analysis , constant coefficients , degree (music) , order (exchange) , partition of unity , mixed finite element method , displacement (psychology) , combinatorics , physics , thermodynamics , computer science , psychology , finance , acoustics , economics , psychotherapist , programming language
In this article, we will discuss the local ultraconvergence of high‐degree finite element method based on a rectangular partition for the second‐degree elliptic problem with constant coefficients Lu ≡ − ∂ ∂ y ia ij∂ u ∂ y j= f yin Ω ⊂ ℜ 2 , u ( y ) = 0 on ∂Ω . Based on suitable regularity, ultraconvergence of the displacement of the extrapolated k th ( k ≥ 3) degree finite element solution has been obtained by an extrapolation technique. Finally, numerical experiments are applied to demonstrate our theoretical findings.