On the Superconvergence of a Conforming Mixed Finite Element for Linear Elasticity on Uniform n-Square Grids

Hongying Man; Shangyou Zhang

doi:10.1007/s42967-025-00476-4

On the Superconvergence of a Conforming Mixed Finite Element for Linear Elasticity on Uniform n-Square Grids

Hongying Man^*
, Shangyou Zhang

^*Corresponding author for this work

School of Mathematics and Statistics

University of Delaware

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

1 Citation (Scopus)

Abstract

This paper is to prove one-order superconvergence of both stress and displacement of a conforming symmetric mixed finite element on uniform n-square grids, for the linear elasticity equation in the Hellinger-Reissner variational formulation. Numerical examples on 2D and 3D uniform square grids are computed, verifying the theory.

Original language	English
Journal	Communications on Applied Mathematics and Computation
DOIs	https://doi.org/10.1007/s42967-025-00476-4
Publication status	Accepted/In press - 2025

Keywords

Conforming finite element
Linear elasticity
Mixed finite element
Square grids
Superconvergence

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10.1007/s42967-025-00476-4

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title = "On the Superconvergence of a Conforming Mixed Finite Element for Linear Elasticity on Uniform n-Square Grids",

abstract = "This paper is to prove one-order superconvergence of both stress and displacement of a conforming symmetric mixed finite element on uniform n-square grids, for the linear elasticity equation in the Hellinger-Reissner variational formulation. Numerical examples on 2D and 3D uniform square grids are computed, verifying the theory.",

keywords = "Conforming finite element, Linear elasticity, Mixed finite element, Square grids, Superconvergence",

author = "Hongying Man and Shangyou Zhang",

note = "Publisher Copyright: {\textcopyright} Shanghai University 2025.",

year = "2025",

doi = "10.1007/s42967-025-00476-4",

language = "English",

journal = "Communications on Applied Mathematics and Computation",

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AU - Man, Hongying

AU - Zhang, Shangyou

N1 - Publisher Copyright: © Shanghai University 2025.

PY - 2025

Y1 - 2025

N2 - This paper is to prove one-order superconvergence of both stress and displacement of a conforming symmetric mixed finite element on uniform n-square grids, for the linear elasticity equation in the Hellinger-Reissner variational formulation. Numerical examples on 2D and 3D uniform square grids are computed, verifying the theory.

AB - This paper is to prove one-order superconvergence of both stress and displacement of a conforming symmetric mixed finite element on uniform n-square grids, for the linear elasticity equation in the Hellinger-Reissner variational formulation. Numerical examples on 2D and 3D uniform square grids are computed, verifying the theory.

KW - Conforming finite element

KW - Linear elasticity

KW - Mixed finite element

KW - Square grids

KW - Superconvergence

UR - https://www.scopus.com/pages/publications/85218982542

U2 - 10.1007/s42967-025-00476-4

DO - 10.1007/s42967-025-00476-4

M3 - Article

AN - SCOPUS:85218982542

SN - 2096-6385

JO - Communications on Applied Mathematics and Computation

JF - Communications on Applied Mathematics and Computation

ER -

On the Superconvergence of a Conforming Mixed Finite Element for Linear Elasticity on Uniform n-Square Grids

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Keywords

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