The stability in 𝐿_{𝑝} and 𝑊¹_{𝑝} of the 𝐿₂-projection onto finite element function spaces

Crouzeix, M.; Thomée, V.

doi:10.1090/S0025-5718-1987-0878688-2

The stability in $L_ p$ and $W^ 1_ p$ of the $L_ 2$-projection onto finite element function spaces
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by M. Crouzeix and V. Thomée PDF

Math. Comp. 48 (1987), 521-532 Request permission

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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