Contributions to Books:

M. Faustmann, J. Melenk, M. Parvizi:
"On the stability of Scott-Zhang type operators and application to multilevel preconditioning in fractal diffusion";
in: "ASC Report 3/2020", issued by: Institute for Analysis and Scientific Computing; Vienna University of Technology, Wien, 2020, ISBN: 978-3-902627-13-1, 1 - 31.

English abstract:
We provide an endpoint stability result for Scott-Zhang type operators in Besov spaces.
For globally continuous piecewise polynomials these are bounded from H3=2 into B3=2 2;1;
for elementwise polynomials these are bounded from H1=2 into B1=2
2;1. As an application,we obtain a multilevel decomposition based on Scott-Zhang operators on a hierarchy of meshes generated by newest vertex bisection with equivalent norms up to (but excluding)
the endpoint case. A local multilevel diagonal preconditioner for the fractional Laplacian on locally re ned meshes with optimal eigenvalue bounds is presented.

Electronic version of the publication:

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