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Mathematics of Computation

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The stability in $L_ p$ and $W^ 1_ p$ of the $L_ 2$-projection onto finite element function spaces


Authors: M. Crouzeix and V. Thomée
Journal: Math. Comp. 48 (1987), 521-532
MSC: Primary 41A15; Secondary 41A35, 65N10, 65N30
DOI: https://doi.org/10.1090/S0025-5718-1987-0878688-2
MathSciNet review: 878688
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Abstract: The stability of the ${L_2}$-projection onto some standard finite element spaces ${V_h}$, considered as a map in ${L_p}$ and $W_p^1$, $1 \leqslant p \leqslant \infty$, is shown under weaker regularity requirements than quasi-uniformity of the triangulations underlying the definitions of the ${V_h}$.


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Article copyright: © Copyright 1987 American Mathematical Society