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arXiv · 2507.06846

A posteriori error estimates for a $C^1$ virtual element method applied to the thin plate vibration problem

Franco Dassi·Andres E. Rubiano·Iván Velásquez
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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 $C^1$ 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.

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Franco Dassi, Andres E. Rubiano, Iván Velásquez. 2025-07-09. A posteriori error estimates for a $C^1$ virtual element method applied to the thin plate vibration problem. https://arxiv.org/abs/2507.06846

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