Contributions to Books:
J. Melenk, T. Wurzer:
"On the stability of the polynomial $L^2$-projection on triangles and tetrahedra";
in: "ASC Report 25/2012",
issued by: Institute for Analysis and Scientific Computing;
Vienna University of Technology,
Wien,
2012,
ISBN: 978-3-902627-05-6,
1
- 37.
English abstract:
For the reference triangle or tetrahedron $T$, we study the stability properties of the $L^2$-projection $\Pi_N$ onto the space of polynomials of degree $N$. We show $\|\Pi_N u\|_{L^2(\partial T)}^2 \leq C \|u\|_{L^2(T)} \|u\|_{H^1(T)}$ and $\|\Pi_N u\|_{H^1(T)} \leq C (N+1)^{1/2} \|u\|_{H^1(T)}$.
This implies optimal convergence rates for the approximation error $\|u - \Pi_N u u\|_{L^2(\partial T)}$ for all $u \in H^k(T)$, $k > 1/2$.
Electronic version of the publication:
http://www.asc.tuwien.ac.at/preprint/2012/asc25x2012.pdf
Created from the Publication Database of the Vienna University of Technology.