Nearly H1-optimal finite element methods

Paul E. Barbone*, Isaac Harari

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


We examine the problem of finding the H1 projection onto a finite element space of an unknown field satisfying a specified boundary value problem. Solving the projection problem typically requires knowing the exact solution. We circumvent this issue and obtain a Petrov-Galerkin formulation which achieves H1 optimality. Requiring weighting functions to be defined locally on the element level permits only approximate H1 optimality in multi-dimensional configurations. We investigate the relation between our formulation and other stabilized FEM formulations. We show, in particular, that our formulation leads to a derivation of the SUPG method. In special cases, the present formulation reduces to that of residual-free bubbles. Finally, we present guidelines for obtaining the Petrov weight functions, and include a numerical example for the Helmholtz equation.

Original languageEnglish
Pages (from-to)5679-5690
Number of pages12
JournalComputer Methods in Applied Mechanics and Engineering
Issue number43-44
StatePublished - 17 Aug 2001


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