A note on the error estimate of the virtual element methods
This work provides a theoretical refinement for numerical analysts working on virtual element methods, but it is an incremental improvement over existing error analysis.
The paper presents a new derivation of optimal-order a priori error estimates for conforming virtual element methods on 3D polyhedral meshes, relaxing geometric assumptions for the energy norm error estimate.
This short note reports a new derivation of the optimal order of the a priori error estimates for conforming virtual element methods (VEM) on 3D polyhedral meshes based on an error equation. The geometric assumptions, which are necessary for the optimal order of the conforming VEM error estimate in the $H^1$-seminorm, are relaxed for that in a bilinear form-induced energy norm.