Ultraconvergence of finite element method by Richardson extrapolation for elliptic problems with inhomogeneous boundary conditions

In this article, Richardson extrapolation technique is employed to investigate the local ultraconvergence properties of Lagrange finite element method using piecewise polynomials of degrees k (k≥2) for the second order elliptic problem with inhomogeneous boundary. A sequence of special graded partit...

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Bibliographic Details
Published inNumerical methods for partial differential equations Vol. 38; no. 1; pp. 33 - 47
Main Authors He, Wen‐ming, Zhao, Ren, Cao, Yong
Format Journal Article
LanguageEnglish
Published Hoboken, USA John Wiley & Sons, Inc 01.01.2022
Wiley Subscription Services, Inc
Subjects
Boundary conditions
Extrapolation
Finite element analysis
Finite element method
graded partition
inhomogeneous boundary
Interpolation
interpolation operator
Polynomials
Richardson extrapolation
ultraconvergence
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Summary:In this article, Richardson extrapolation technique is employed to investigate the local ultraconvergence properties of Lagrange finite element method using piecewise polynomials of degrees k (k≥2) for the second order elliptic problem with inhomogeneous boundary. A sequence of special graded partition TNs are proposed and a new interpolation operator is introduced to achieve 2k order local ultraconvergence for the displacement and derivative.
Bibliography:Funding information
Wen‐ming He and Ren Zhao contributed equally to this work and also regarded as co‐first authors.
Guangdong Basic and Applied Basic Research Foundation, 2019A1515110835; National Natural Science Foundation of China, 11671304; 11771338; Shenzhen Technology Projects, ZDSYS201707280904031
ISSN:0749-159X
1098-2426
DOI:10.1002/num.22822