Quasi-optimal stability estimates for the hp-Raviart-Thomas projection operator on the cube

Alexey Chernov (University of Reading)

Frank Adams Room 2, Alan Turing Building,

Stability of the hp-Raviart-Thomas projection operator as a mapping H^1(K) -> H^1(K) on the unit cube K in R^3 has been addressed e.g. in [2], see also [1]. These results are suboptimal w.r.t. the polynomial degree. In this talk we present quasi-optimal stability estimates for the hp-Raviart-Thomas projection operator on the cube. The analysis involves elements of the polynomial approximation theory on an interval and the K-method of Banach space interpolation. No a priori knowledge on these topics will be assumed.

(Joint work with Herbert Egger, TU Darmstadt) 

[1] Mark Ainsworth and Katia Pinchedez. hp-approximation theory for BDFM and RT finite elements on quadrilaterals. SIAM J. Numer. Anal., 40(6):2047–2068 (electronic) (2003), 2002. 

[2] Dominik Schötzau, Christoph Schwab, and Andrea Toselli. Mixed hp-DGFEM for incompressible flows. SIAM J. Numer. Anal., 40(6):2171–2194 (electronic) (2003), 2002.

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