Remote Access Mathematics of Computation
Green Open Access

Mathematics of Computation

ISSN 1088-6842(online) ISSN 0025-5718(print)

 

 

Smoothed projections in finite element exterior calculus


Authors: Snorre H. Christiansen and Ragnar Winther
Journal: Math. Comp. 77 (2008), 813-829
MSC (2000): Primary 65N30, 53A45
DOI: https://doi.org/10.1090/S0025-5718-07-02081-9
Published electronically: December 20, 2007
MathSciNet review: 2373181
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: The development of smoothed projections, constructed by combining the canonical interpolation operators defined from the degrees of freedom with a smoothing operator, has proved to be an effective tool in finite element exterior calculus. The advantage of these operators is that they are $ L^2$ bounded projections, and still they commute with the exterior derivative. In the present paper we generalize the construction of these smoothed projections, such that also non-quasi-uniform meshes and essential boundary conditions are covered. The new tool introduced here is a space-dependent smoothing operator that commutes with the exterior derivative.


References [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Mathematics of Computation with MSC (2000): 65N30, 53A45

Retrieve articles in all journals with MSC (2000): 65N30, 53A45


Additional Information

Snorre H. Christiansen
Affiliation: Centre of Mathematics for Applications and Department of Mathematics, University of Oslo, P.O. Box 1053, Blindern, 0316 Oslo, Norway
Email: snorrec@cma.uio.no

Ragnar Winther
Affiliation: Centre of Mathematics for Applications and Department of Informatics, University of Oslo, P.O. Box 1053, Blindern, 0316 Oslo, Norway
Email: ragnar.winther@cma.uio.no

DOI: https://doi.org/10.1090/S0025-5718-07-02081-9
Keywords: Exterior calculus, finite elements, interpolation operators
Received by editor(s): December 20, 2006
Received by editor(s) in revised form: March 22, 2007
Published electronically: December 20, 2007
Additional Notes: This research was supported by the Norwegian Research Council. The first author acknowledges that this work, conducted as part of the award “Numerical analysis and simulations of geometric wave equations” made under the European Heads of Research Councils and European Science Foundation EURYI (European Young Investigator) Awards scheme, was supported by funds from the Participating Organizations of EURYI and the EC Sixth Framework Program.
Article copyright: © Copyright 2007 American Mathematical Society