Virtual Element Methods on Meshes with Small Edges or Faces
arXiv:1710.00442189 citationsh-index: 42
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It provides theoretical guarantees for virtual element methods on challenging meshes, benefiting numerical analysts working on polygonal/polyhedral discretizations.
The paper establishes error estimates for virtual element methods on meshes with small edges or faces, proving optimal convergence rates for the Poisson problem in 2D and 3D.
We consider a model Poisson problem in $\R^d$ ($d=2,3$) and establish error estimates for virtual element methods on polygonal or polyhedral meshes that can contain small edges ($d=2$) or small faces ($d=3$).