Publications in Scientific Journals:
M. Faustmann, J. Melenk, M. Parvizi:
"On the stability of Scott-Zhang type operators and application to multilevel preconditioning in fractional diffusion";
ESAIM: Mathematical Modelling and Numerical Analysis,
55
(2021),
595
- 625.
English abstract:
Abstract . We provide an endpoint stability result for Scott-Zhang type operators in Besov spaces. For globally continuous piecewise polynomials these are bounded from H ^3/2 into B^3/2_2,∞; for element-wise polynomials these are bounded from H^1/2 into B^1/2_2,∞.
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 refined meshes with optimal eigenvalue
bounds is presented.
"Official" electronic version of the publication (accessed through its Digital Object Identifier - DOI)
http://dx.doi.org/10.1051/m2an/2020079
Created from the Publication Database of the Vienna University of Technology.