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arXiv · 2105.11621

Optimal maximum norm estimates for virtual element methods

Wen-Ming He·Hailong Guo
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Abstract

The maximum norm error estimations for virtual element methods are studied. To establish the error estimations, we prove higher local regularity based on delicate analysis of Green's functions and high-order local error estimations for the partition of the virtual element solutions. The maximum norm of the exact gradient and the gradient of the projection of the virtual element solutions are proved to achieve optimal convergence results. For high-order virtual element methods, we establish the optimal convergence results in $L^{\infty}$ norm. Our theoretical discoveries are validated by a numerical example on general polygonal meshes.

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Wen-Ming He, Hailong Guo. 2021-05-25. Optimal maximum norm estimates for virtual element methods. https://doi.org/10.1137/21m1420186

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