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,
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.