A note on the error estimate of the virtual element methods
Shuhao Cao, Long Chen, Frank Lin
TL;DR
This paper presents a new derivation of optimal error estimates for conforming virtual element methods on 3D polyhedral meshes, relaxing geometric assumptions for certain norms.
Contribution
It introduces a novel derivation approach for error estimates, relaxing geometric assumptions for the energy norm in 3D VEM.
Findings
Optimal error estimates derived for conforming VEM in 3D
Relaxed geometric assumptions for energy norm error estimates
Enhanced understanding of VEM error behavior on polyhedral meshes
Abstract
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 -seminorm, are relaxed for that in a bilinear form-induced energy norm.
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Taxonomy
TopicsAdvanced Numerical Methods in Computational Mathematics · Electromagnetic Simulation and Numerical Methods · Numerical methods in engineering