On the stability of the L-2 projection in H-1(Omega) Academic Article

abstract

• 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.

authors

• Pasciak, Joseph

published proceedings

• MATHEMATICS OF COMPUTATION

author list (cited authors)

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

citation count

• 104

complete list of authors

• Bramble, JH||Pasciak, JE||Steinbach, O

publication date

• May 2002

publisher

• American Mathematical Society (AMS)  Publisher

published in

• Mathematics of Computation  Journal

keywords

• Adaptivity
• Finite Elements
• L-2 Projection
• STABILITY

Digital Object Identifier (DOI)

• 10.1090/s0025-5718-01-01314-x

start page

• 147

end page

• 156

volume

• 71

issue

• 237

URL

• http://dx.doi.org/10.1090/s0025-5718-01-01314-x