On the stability of the $L^2$ projection in $H^1(Omega)$ Academic Article uri icon


  • 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.

published proceedings

  • Mathematics of Computation

author list (cited authors)

  • Bramble, J. H., Pasciak, J. E., & Steinbach, O.

citation count

  • 101

complete list of authors

  • Bramble, James H||Pasciak, Joseph E||Steinbach, Olaf

publication date

  • May 2001