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

2023/03/10 by Xianlin Jin, Shuonan Wu, Jin, Xianlin +1 · 1 citation
Engineering · Mathematics · #65N30 #Advanced Numerical Methods in Computational Mathematics #Differential Equations and Numerical Methods #FOS: Mathematics #Numerical Analysis (math.NA) #Numerical methods in engineering

paper · pdf · doi:10.48550/arxiv.2303.05784

openalex publication_date 2023/03/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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 H³ problems, we establish the quasi-optimal error estimate for the tri-harmonic equation in the broken H³ norm of any dimension. The theoretical results are validated further by the numerical tests in both 2D and 3D situations.

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• Nonconforming Linear Element Method for a Generalized Tensor-Valued Stokes Equation with Application to the Triharmonic Equation

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