Two families of $n$-rectangle nonconforming finite elements for sixth-order elliptic equations

In this paper, we propose two families of nonconforming finite elements on $n$-rectangle meshes of any dimension to solve the sixth-order elliptic equations. The unisolvent property and the approximation ability of the new finite element spaces are established. A new mechanism, called the exchange o...

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Bibliographic Details
Main Authors Jin, Xianlin, Wu, Shuonan
Format Journal Article
LanguageEnglish
Published 10.03.2023
Subjects
Computer Science - Numerical Analysis
Mathematics - Numerical Analysis
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Summary:In this paper, we propose two families of nonconforming finite elements on $n$-rectangle meshes of any dimension to solve the sixth-order elliptic equations. The unisolvent property and the approximation ability of the new finite element spaces are established. A new mechanism, called the exchange of sub-rectangles, for investigating the weak continuities of the proposed elements is discovered. With the help of some conforming relatives for the $H^3$ problems, we establish the quasi-optimal error estimate for the tri-harmonic equation in the broken $H^3$ norm of any dimension. The theoretical results are validated further by the numerical tests in both 2D and 3D situations.
DOI:10.48550/arxiv.2303.05784