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:

Created from the Publication Database of the Vienna University of Technology.