A posteriori error estimates for a $C^1$ virtual element method applied to the thin plate vibration problem
Numerical Analysis
2025-07-10 v1 Numerical Analysis
Abstract
We propose and analyse residual-based a posteriori error estimates for the virtual element discretisation applied to the thin plate vibration problem in both two and three dimensions. Our approach involves a conforming discrete formulation suitable for meshes composed of polygons and polyhedra. The reliability and efficiency of the error estimator are established through a dimension-independent proof. Finally, several numerical experiments are reported to demonstrate the optimal performance of the method in 2D and 3D.
Cite
@article{arxiv.2507.06846,
title = {A posteriori error estimates for a $C^1$ virtual element method applied to the thin plate vibration problem},
author = {Franco Dassi and Andres E. Rubiano and Iván Velásquez},
journal= {arXiv preprint arXiv:2507.06846},
year = {2025}
}