Optimal convergence estimates for the trace of the polynomial L2-projection operator on a simplexChernov, A. (2012) Optimal convergence estimates for the trace of the polynomial L2-projection operator on a simplex. Mathematics of Computation, 81 (278). pp. 765-787. ISSN 1088-6842
It is advisable to refer to the publisher's version if you intend to cite from this work. See Guidance on citing. To link to this item DOI: 10.1090/S0025-5718-2011-02513-5 Abstract/SummaryIn this paper we study convergence of the L2-projection onto the space of polynomials up to degree p on a simplex in Rd, d >= 2. Optimal error estimates are established in the case of Sobolev regularity and illustrated on several numerical examples. The proof is based on the collapsed coordinate transform and the expansion into various polynomial bases involving Jacobi polynomials and their antiderivatives. The results of the present paper generalize corresponding estimates for cubes in Rd from [P. Houston, C. Schwab, E. Süli, Discontinuous hp-finite element methods for advection-diffusion-reaction problems. SIAM J. Numer. Anal. 39 (2002), no. 6, 2133-2163].
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