On the sharpness of certain local estimates for *H* projections into finite element spaces: influence of a re-entrant corner

Author:
Lars B. Wahlbin

Journal:
Math. Comp. **42** (1984), 1-8

MSC:
Primary 65N30; Secondary 65N15

DOI:
https://doi.org/10.1090/S0025-5718-1984-0725981-7

MathSciNet review:
725981

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Abstract: In a plane polygonal domain with a reentrant corner, consider a homogeneous Dirichlet problem for Poisson's equation 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 comparable to *h*, . Assuming that *u* has a singularity of the type at the vertex of maximal angle , we show: (i) For any subdomain *A* and any *s*, the error measured in is not better than . (ii)On annular strips of points of distance of order *d* from , the pointwise error is not better than .

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DOI:
https://doi.org/10.1090/S0025-5718-1984-0725981-7

Article copyright:
© Copyright 1984
American Mathematical Society