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Evaluating local approximations of the L^2-orthogonal projection between non-nested finite element spaces

Informazioni aggiuntive

Autori
Dickopf T.
Tipo
Articolo pubblicato in rivista scientifica
Anno
2014
Lingua
Inglese
Abstract
We present quantitative studies of transfer operators between finite element spaces associated with unrelated meshes. Several local approximations of the global L2-orthogonal projection are reviewed and evaluated computationally. The numerical studies in 3D provide the first estimates of the quantitative differences between a range of transfer operators between non-nested finite element spaces. We consider the standard finite element interpolation, Clément’s quasi-interpolation with different local polynomial degrees, the global L2-orthogonal projection, a local L2-quasi-projection via a discrete inner product, and a pseudo-L2-projection defined by a Petrov-Galerkin variational equation with a discontinuous test space. Understanding their qualitative and quantitative behaviors in this computational way is interesting per se; it could also be relevant in the context of discretization and solution techniques which make use of different non-nested meshes. It turns out that the pseudo-L2-projection approximates the actual L2-orthogonal projection best. The obtained results seem to be largely independent of the underlying computational domain; this is demonstrated by four examples (ball, cylinder, half torus and Stanford Bunny).
Rivista
Numerical Mathematics: Theory, Methods, and Applications
Volume
7
Numero
3
Pagina inizio
288
Pagina fine
316