CutIGA with Least Squares Stabilized Nitsche Boundary Conditions: The Biharmonic Problem
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 H4(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≥4 give energy and L2 error bounds of orders hp−1 and hp+1. We also analyze a face-stabilized extension to C1 splines of degree p=2 and C2 splines of degree p=3. Exact-ellipse experiments examine convergence, cut stability, and parameter sensitivity.
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BibTeX
@misc{larson2026cutiga,
title = {{CutIGA with Least Squares Stabilized Nitsche Boundary Conditions: The Biharmonic Problem}},
author = {Mats G. Larson and Karl Larsson},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.11636},
eprint = {2610.11636},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.11636},
}
RIS
TY - UNPB
TI - CutIGA with Least Squares Stabilized Nitsche Boundary Conditions: The Biharmonic Problem
AU - Mats G. Larson
AU - Karl Larsson
PY - 2026
DA - 2026/10/08
PB - arXiv
DO - 10.48550/arxiv.2610.11636
UR - https://arxiv.org/abs/2610.11636
AB - 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≥4 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.
ER -