On the stability of the $L^2$ projection in $H^1(\Omega)$
On the stability of the $L^2$ projection in $H^1(\Omega)$
We prove the stability in $H^1(\Omega )$ of the $L^2$ projection onto a family of finite element spaces of conforming piecewise linear functions satisfying certain local mesh conditions. We give explicit formulae to check these conditions for a given finite element mesh in any number of spatial dimensions. In particular, …