Partial differential equations, Maxwell equations, Polynomials, Electromagnetic theory
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 spectralmixed methods, including the Raviart–Thomas method and mixed formulations of Maxwell equations. We also prove some discrete Friedrichs type inequalities involving curl.
Gopalakrishnan, Jay and Demkowicz, Leszek, "Quasioptimality of Some Spectral Mixed Methods" (2004). Mathematics and Statistics Faculty Publications and Presentations. 68.
NOTICE: this is the author’s version of a work that was accepted for publication in Journal of Computational & Applied Mathematics. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published in Journal of Computational & Applied Mathematics, [VOL 167, ISSUE 1, May 2004]. doi:10.1016/j.cam.2003.10.001