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

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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 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.

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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