Optimal convergence estimates for the trace of the polynomial L2-projection operator on a simplex

Chernov, 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 doi: 10.1090/S0025-5718-2011-02513-5

Abstract/Summary

In 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].

Item Type	Article
URI	https://reading-clone.eprints-hosting.org/id/eprint/33215
Identification Number/DOI	10.1090/S0025-5718-2011-02513-5
Refereed	Yes
Divisions	No Reading authors. Back catalogue items Science > School of Mathematical, Physical and Computational Sciences > Department of Mathematics and Statistics
Publisher	American Mathematical Society
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