A posteriori error estimates for a C¹ virtual element method applied to the thin plate vibration problem.

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 C¹ 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.