Some Estimates for Virtual Element Methods in Three Dimensions

Comput. Methods Appl. Math.（2023）

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Abstract

Some estimates on virtual element methods (VEMs), including inverse inequalities, norm equivalence, and interpolation error estimates, are developed for star-shaped polyhedral meshes whose faces admit virtual regular and quasi-uniform triangulations. This mesh regularity covers the usual ones used for theoretical analysis of VEMs, and the proofs are carried out in a straightforward way.

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Key words

Virtual Element Method,Polyhedral Meshes,Inverse Inequality,Norm Equivalence,Interpolation Error Estimates

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