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

Wen ming He; Ren Zhao; Yong Cao

doi:10.1002/num.22822

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

Wen ming He
, Ren Zhao^*
, Yong Cao

^*Corresponding author for this work

Lingnan Normal University
Harbin Institute of Technology Shenzhen

Research output: Contribution to journal › Article › peer-review

Abstract

In this article, Richardson extrapolation technique is employed to investigate the local ultraconvergence properties of Lagrange finite element method using piecewise polynomials of degrees (Formula presented.) ((Formula presented.)) for the second order elliptic problem with inhomogeneous boundary. A sequence of special graded partition (Formula presented.) are proposed and a new interpolation operator is introduced to achieve (Formula presented.) order local ultraconvergence for the displacement and derivative.

Original language	English
Pages (from-to)	33-47
Number of pages	15
Journal	Numerical Methods for Partial Differential Equations
Volume	38
Issue number	1
DOIs	https://doi.org/10.1002/num.22822
State	Published - Jan 2022
Externally published	Yes

Keywords

Richardson extrapolation
graded partition
inhomogeneous boundary
interpolation operator
ultraconvergence

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10.1002/num.22822

Cite this

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title = "Ultraconvergence of finite element method by Richardson extrapolation for elliptic problems with inhomogeneous boundary conditions",

abstract = "In this article, Richardson extrapolation technique is employed to investigate the local ultraconvergence properties of Lagrange finite element method using piecewise polynomials of degrees (Formula presented.) ((Formula presented.)) for the second order elliptic problem with inhomogeneous boundary. A sequence of special graded partition (Formula presented.) are proposed and a new interpolation operator is introduced to achieve (Formula presented.) order local ultraconvergence for the displacement and derivative.",

keywords = "Richardson extrapolation, graded partition, inhomogeneous boundary, interpolation operator, ultraconvergence",

author = "He, \{Wen ming\} and Ren Zhao and Yong Cao",

note = "Publisher Copyright: {\textcopyright} 2021 Wiley Periodicals LLC.",

year = "2022",

month = jan,

doi = "10.1002/num.22822",

language = "英语",

volume = "38",

pages = "33--47",

journal = "Numerical Methods for Partial Differential Equations",

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T1 - Ultraconvergence of finite element method by Richardson extrapolation for elliptic problems with inhomogeneous boundary conditions

AU - He, Wen ming

AU - Zhao, Ren

AU - Cao, Yong

PY - 2022/1

Y1 - 2022/1

N2 - In this article, Richardson extrapolation technique is employed to investigate the local ultraconvergence properties of Lagrange finite element method using piecewise polynomials of degrees (Formula presented.) ((Formula presented.)) for the second order elliptic problem with inhomogeneous boundary. A sequence of special graded partition (Formula presented.) are proposed and a new interpolation operator is introduced to achieve (Formula presented.) order local ultraconvergence for the displacement and derivative.

AB - In this article, Richardson extrapolation technique is employed to investigate the local ultraconvergence properties of Lagrange finite element method using piecewise polynomials of degrees (Formula presented.) ((Formula presented.)) for the second order elliptic problem with inhomogeneous boundary. A sequence of special graded partition (Formula presented.) are proposed and a new interpolation operator is introduced to achieve (Formula presented.) order local ultraconvergence for the displacement and derivative.

KW - Richardson extrapolation

KW - graded partition

KW - inhomogeneous boundary

KW - interpolation operator

KW - ultraconvergence

UR - https://www.scopus.com/pages/publications/85109391701

U2 - 10.1002/num.22822

DO - 10.1002/num.22822

M3 - 文章

AN - SCOPUS:85109391701

SN - 0749-159X

VL - 38

SP - 33

EP - 47

JO - Numerical Methods for Partial Differential Equations

JF - Numerical Methods for Partial Differential Equations

IS - 1

ER -

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

Abstract

Keywords

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