Continuous Linear Finite Element Method for Biharmonic Problems on Surfaces
Numerical Analysis
2024-04-30 v1 Numerical Analysis
Abstract
This paper presents an innovative continuous linear finite element approach to effectively solve biharmonic problems on surfaces. The key idea behind this method lies in the strategic utilization of a surface gradient recovery operator to compute the second-order surface derivative of a piecewise continuous linear function defined on the approximate surface, as conventional notions of second-order derivatives are not directly applicable in this context. By incorporating appropriate stabilizations, we rigorously establish the stability of the proposed formulation. Despite the presence of geometric error, we provide optimal error estimates in both the energy norm and norm. Theoretical results are supported by numerical experiments.
Cite
@article{arxiv.2404.17958,
title = {Continuous Linear Finite Element Method for Biharmonic Problems on Surfaces},
author = {Ying Cai and Hailong Guo and Zhimin Zhang},
journal= {arXiv preprint arXiv:2404.17958},
year = {2024}
}