A novel H(div div)-conforming finite element is presented, redistributing degrees of freedom to edges and faces. This method enables efficient numerical solutions for the biharmonic equation. The redistribution process involves transferring vertex and normal plane DoFs to faces and edges. By redistributing these DoFs, a hybridizable mixed method with superconvergence is achieved. The proposed finite element space ensures minimal continuity requirements while offering optimal convergence rates for symmetric tensors. Additionally, new weak Galerkin and C0 discontinuous Galerkin methods are derived for the biharmonic equation in all dimensions. The implementation of this method as a generalization of hybridized HHJ methods from 2D to arbitrary dimensions shows promising results.
To Another Language
from source content
arxiv.org
Key Insights Distilled From
by Long Chen,Xu... at arxiv.org 03-18-2024
https://arxiv.org/pdf/2305.11356.pdfDeeper Inquiries