The stability in $L\sb p$ and $W\sp 1\sb p$ of the $L\sb 2$-projection onto finite element function spaces

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 ${V_h}$.