The stability in and of the projection onto finite element function spaces
Authors:
M. Crouzeix and V. Thomée
Journal:
Math. Comp. 48 (1987), 521532
MSC:
Primary 41A15; Secondary 41A35, 65N10, 65N30
MathSciNet review:
878688
Fulltext PDF Free Access
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Abstract: The stability of the projection onto some standard finite element spaces , considered as a map in and , , is shown under weaker regularity requirements than quasiuniformity of the triangulations underlying the definitions of the .
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 C. Bernardi & G. Raugel, "Approximation numérique de certaines équations paraboliques non linéaires," RAIRO Anal. Numér., v. 18, 1984, pp. 237285. MR 751759 (86a:65097)
 [2]
 C. de Boor, "A bound on the norm of approximation by splines in terms of a global mesh ratio," Math. Comp., v. 30, 1976, pp. 765771. MR 0425432 (54:13387)
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 A. H. Schatz, V. Thomée & L. B. Wahlbin, "Maximum norm stability and error estimates in parabolic finite element equations," Comm. Pure Appl. Math., v. 33, 1980, pp. 265304. MR 562737 (81g:65136)
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 G. O. Thorin, "Convexity theorems generalizing those of M. Riesz and Hadamard with some applications," Medd. Lunds Univ. Mat. Sem., v. 9, 1948, pp. 158. MR 0025529 (10:21e)
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Additional Information
DOI:
http://dx.doi.org/10.1090/S00255718198708786882
PII:
S 00255718(1987)08786882
Article copyright:
© Copyright 1987
American Mathematical Society
