A NEW MIXED FINITE ELEMENT FOR THE LINEAR ELASTICITY PROBLEM IN 3D

Jun Hu; Rui Ma; Yuanxun Sun

doi:10.4208/jcm.2405-m2023-0051

A NEW MIXED FINITE ELEMENT FOR THE LINEAR ELASTICITY PROBLEM IN 3D

Jun Hu
, Rui Ma
, Yuanxun Sun^*

^*Corresponding author for this work

School of Mathematics and Statistics

Peking University

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

Abstract

This paper constructs the first mixed finite element for the linear elasticity problem in 3D using P₃ polynomials for the stress and discontinuous P₂ polynomials for the displace-ment on tetrahedral meshes under some mild mesh conditions. The degrees of freedom of the stress space as well as the corresponding nodal basis are established by characterizing a space of certain piecewise constant symmetric matrices on a patch around each edge. Macro-element techniques are used to define a stable interpolation to prove the discrete inf-sup condition. Optimal convergence is obtained theoretically.

Original language	English
Pages (from-to)	1444-1468
Number of pages	25
Journal	Journal of Computational Mathematics
Volume	43
Issue number	6
DOIs	https://doi.org/10.4208/jcm.2405-m2023-0051
Publication status	Published - 31 Oct 2025

Keywords

Discrete inf-sup condition
Linear elasticity
Lower order mixed elements
Macro-element techniques

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10.4208/jcm.2405-m2023-0051

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abstract = "This paper constructs the first mixed finite element for the linear elasticity problem in 3D using P3 polynomials for the stress and discontinuous P2 polynomials for the displace-ment on tetrahedral meshes under some mild mesh conditions. The degrees of freedom of the stress space as well as the corresponding nodal basis are established by characterizing a space of certain piecewise constant symmetric matrices on a patch around each edge. Macro-element techniques are used to define a stable interpolation to prove the discrete inf-sup condition. Optimal convergence is obtained theoretically.",

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author = "Jun Hu and Rui Ma and Yuanxun Sun",

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N2 - This paper constructs the first mixed finite element for the linear elasticity problem in 3D using P3 polynomials for the stress and discontinuous P2 polynomials for the displace-ment on tetrahedral meshes under some mild mesh conditions. The degrees of freedom of the stress space as well as the corresponding nodal basis are established by characterizing a space of certain piecewise constant symmetric matrices on a patch around each edge. Macro-element techniques are used to define a stable interpolation to prove the discrete inf-sup condition. Optimal convergence is obtained theoretically.

AB - This paper constructs the first mixed finite element for the linear elasticity problem in 3D using P3 polynomials for the stress and discontinuous P2 polynomials for the displace-ment on tetrahedral meshes under some mild mesh conditions. The degrees of freedom of the stress space as well as the corresponding nodal basis are established by characterizing a space of certain piecewise constant symmetric matrices on a patch around each edge. Macro-element techniques are used to define a stable interpolation to prove the discrete inf-sup condition. Optimal convergence is obtained theoretically.

KW - Discrete inf-sup condition

KW - Linear elasticity

KW - Lower order mixed elements

KW - Macro-element techniques

UR - https://www.scopus.com/pages/publications/105022429360

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JO - Journal of Computational Mathematics

JF - Journal of Computational Mathematics

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A NEW MIXED FINITE ELEMENT FOR THE LINEAR ELASTICITY PROBLEM IN 3D

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