On the sharpness of certain local estimates for H projections into finite element spaces: influence of a reentrant corner
Author:
Lars B. Wahlbin
Journal:
Math. Comp. 42 (1984), 18
MSC:
Primary 65N30; Secondary 65N15
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 quasiuniform (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:
http://dx.doi.org/10.1090/S00255718198407259817
PII:
S 00255718(1984)07259817
Article copyright:
© Copyright 1984
American Mathematical Society
