Smoothed projections in finite element exterior calculus

Christiansen, Snorre; Winther, Ragnar

doi:10.1090/S0025-5718-07-02081-9

Smoothed projections in finite element exterior calculus
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by Snorre H. Christiansen and Ragnar Winther;

Math. Comp. 77 (2008), 813-829

DOI: https://doi.org/10.1090/S0025-5718-07-02081-9

Published electronically: December 20, 2007

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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.

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