Skip to Main Content

Mathematics of Computation

Published by the American Mathematical Society since 1960 (published as Mathematical Tables and other Aids to Computation 1943-1959), Mathematics of Computation is devoted to research articles of the highest quality in computational mathematics.

ISSN 1088-6842 (online) ISSN 0025-5718 (print)

The 2020 MCQ for Mathematics of Computation is 1.78.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.

 

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

by Lars B. Wahlbin PDF
Math. Comp. 42 (1984), 1-8 Request permission

Abstract:

In a plane polygonal domain with a reentrant corner, consider a homogeneous Dirichlet problem for Poisson’s equation $- \Delta u = f$ 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 comparable to h, $0 < h \leqslant 1$. Assuming that u has a singularity of the type $|x - {v_M}{|^\beta }$ at the vertex ${v_M}$ of maximal angle $\pi /\beta$, we show: (i) For any subdomain A and any s, the error measured in ${H^{ - s}}(A)$ is not better than $O({h^{2\beta }})$. (ii)On annular strips of points of distance of order d from ${v_M}$, the pointwise error is not better than $O({h^{2\beta }}{d^{ - \beta }})$.
References
Similar Articles
  • Retrieve articles in Mathematics of Computation with MSC: 65N30, 65N15
  • Retrieve articles in all journals with MSC: 65N30, 65N15
Additional Information
  • © Copyright 1984 American Mathematical Society
  • 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