## On the stability of the boundary trace of the polynomial L2-projection on triangles and tetrahedra

- Jens Markus Melenk, T. Wurzer
- Computers & Mathematics with Applications
- 2014

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@article{Chernov2012OptimalCE, title={Optimal convergence estimates for the trace of the polynomial L2-projection operator on a simplex}, author={Alexey Chernov}, journal={Math. Comput.}, year={2012}, volume={81}, pages={765-787} }

- Published 2012 in Math. Comput.
DOI:10.1090/S0025-5718-2011-02513-5

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… CONTINUE READING