Nearly H1-optimal finite element methods

✍ Scribed by Paul E. Barbone; Isaac Harari

• Book ID: 104266812
• Publisher: Elsevier Science
• Year: 2001
• Tongue: English
• Weight: 144 KB
• Volume: 190
• Category: Article
• ISSN: 0045-7825
• DOI: 10.1016/s0045-7825(01)00191-8

✦ Synopsis

We examine the problem of ®nding the H 1 projection onto a ®nite element space of an unknown ®eld satisfying a speci®ed 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 H 1 optimality. Requiring weighting functions to be de®ned locally on the element level permits only approximate H 1 optimality in multi-dimensional con®gurations. 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.