A TraceFEM $C^0$ Interior Penalty Method for the Surface Biharmonic Equation
Numerical Analysis
2025-12-23 v1 Numerical Analysis
Abstract
We construct and analyze a TraceFEM discretization for the surface biharmonic problem. The method utilizes standard quadratic Lagrange finite element spaces defined on a three-dimensional background mesh and a symmetric interior penalty formulation posed on a second-order polyhedral approximation of the surface. Stability is achieved through a combination of surface edge penalties and bulk-facet penalization of gradient and Hessian jumps. We prove optimal first-order convergence in a discrete norm and quadratic convergence in the norm.
Cite
@article{arxiv.2512.18949,
title = {A TraceFEM $C^0$ Interior Penalty Method for the Surface Biharmonic Equation},
author = {Michael Neilan and Hongzhi Wan},
journal= {arXiv preprint arXiv:2512.18949},
year = {2025}
}