Quasioptimality of some spectral mixed methods

Authors:
Jayadeep Gopalakrishnan;Leszek F. Demkowicz
Affiliations:
Department of Mathematics, University of Florida, 358 Little Hall, Gainesville, FL;Department of Aerospace Engineering and Engineering Mechanics, The University of Texas, Austin, TX
Venue:
Journal of Computational and Applied Mathematics
Year:
2004

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Abstract

In this paper, we construct a sequence of projectors into certain polynomial spaces satisfying a commuting diagram property with norm bounds independent of the polynomial degree. Using the projectors, we obtain quasioptimality of some spectral mixed methods, including the Raviart-Thomas method and mixed formulations of Maxwell equations. We also prove some discrete Friedrichs type inequalities involving curl.