Optimal Convergence Estimates for the Trace of the Polynomial L-projection Operator on a Simplex
نویسنده
چکیده
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 advectiondiffusion-reaction problems. SIAM J. Numer. Anal. 39 (2002), no. 6, 2133– 2163].
منابع مشابه
Optimal convergence estimates for the trace of the polynomial L2-projection operator on a simplex
Article Accepted Version Chernov, A. (2012) Optimal convergence estimates for the trace of the polynomial L2-projection operator on a simplex. It is advisable to refer to the publisher's version if you intend to cite from the work. All outputs in CentAUR are protected by Intellectual Property Rights law, including copyright law. Copyright and IPR is retained by the creators or other copyright h...
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تاریخ انتشار 2010