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Evaluating Local Approximations of the L2-Orthogonal Projection Between Non-Nested Finite Element Spaces

Published online by Cambridge University Press:  28 May 2015

Thomas Dickopf  and
Rolf Krause
Thomas Dickopf*
Affiliation:
Università della Svizzera italiana (USI, University of Lugano), Institute of Computational Science, Via G. Buffi 13, 6904 Lugano, Switzerland
Rolf Krause*
Affiliation:
Università della Svizzera italiana (USI, University of Lugano), Institute of Computational Science, Via G. Buffi 13, 6904 Lugano, Switzerland
*
Corresponding author.Email address:thomas.dickopf@usi.ch
Corresponding author.Email address:thomas.dickopf@usi.ch
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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).

Keywords

65D0565F1065N3065N5065N55Finite elementsunstructured meshesnon-nested spacestransfer operatorsinterpolationprojection
Type
Research Article
Information
Numerical Mathematics: Theory, Methods and Applications , Volume 7 , Issue 3 , August 2014 , pp. 288 - 316
Copyright
Copyright © Global Science Press Limited 2014

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