A posteriori error estimates for a $$C^1$$ virtual element method applied to the thin plate vibration problem.
Abstract
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 $$C^1$$ 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.
Fields of Study & Subjects
Advanced Numerical Methods in Computational Mathematics
Matrix Theory and Algorithms
Contact Mechanics and Variational Inequalities
Publication details
- Journal / source
- Advances in Computational Mathematics
- Publisher
- Springer Science and Business Media LLC
- Volume
- 52
- Issue
- 2
- Publication date
- 23 February 2026
- Language
- EN