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On the quasi-optimality in $ L\sb{\infty }$ of the $ \dot H\sp{1}$-projection into finite element spaces


Authors: A. H. Schatz and L. B. Wahlbin
Journal: Math. Comp. 38 (1982), 1-22
MSC: Primary 65N30
DOI: https://doi.org/10.1090/S0025-5718-1982-0637283-6
MathSciNet review: 637283
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Abstract: The $ {\dot{H}^1}$-projection into finite element spaces based on quasi-uniform partitions of a bounded smooth domain in $ {R^N}$, $ N \geqslant 2$ arbitrary, is shown to be stable in the maximum norm (or, in the case of piecewise linear or bilinear functions, almost stable). It is not assumed that the mesh-domains coincide with the basic domain.


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DOI: https://doi.org/10.1090/S0025-5718-1982-0637283-6
Article copyright: © Copyright 1982 American Mathematical Society