Year: 2026
Type: preprint
Abstract: We propose a symmetric Nitsche method for the biharmonic Dirichlet problem on a smooth domain whose boundary may cut arbitrarily through the computational mesh. Bulk least-squares stabilization in a boundary strip and tangential boundary penalties control the consistency terms through an explicit lifting of the two Dirichlet traces. This gives coercivity on $H^4(Ω)$ without inverse inequalities and permits a fixed penalty independent of the cut configuration for sufficiently thin strips. Under suitable regularity assumptions, splines of degree $p\geq4$ give energy and $L^2$ error bounds of orders $h^{p-1}$ and $h^{p+1}$. We also analyze a face-stabilized extension to $C^1$ splines of degree $p=2$ and $C^2$ splines of degree $p=3$. Exact-ellipse experiments examine convergence, cut stability, and parameter sensitivity.
Source: arXiv (Cornell University)
Authors: Larson, Mats G., Larsson, Karl
Language: English
Subfield: Computational Mechanics
Field: Engineering
Domain: Physical Sciences
Open Access status: green
Funder: Vetenskapsrådet
OpenAlex ID: W7221146061