On the stability of the $L^2$ projection in $H^1(Omega)$
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We prove the stability in H1() of the L2projection 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, stability of the L2projection in H1() holds for locally quasiuniform geometrically refined meshes as long as the volume of neighboring elements does not change too drastically.
Mathematics of Computation
author list (cited authors)
Bramble, J. H., Pasciak, J. E., & Steinbach, O.
complete list of authors
Bramble, James H||Pasciak, Joseph E||Steinbach, Olaf