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In a plane polygonal domain with a reentrant corner, consider a homogeneous Dirichlet problem for Poisson's equation -Au = f with f smooth and the corresponding Galerkin finite element solutions in a family of piecewise polynomial spaces based on quasi-uniform (uniformly regular) triangulations with the diameter of each element compara-

On the sharpness of certain local estimates for $\text{\textit{\r H}}^1$ projections into finite element spaces: influence of a re-entrant corner