期刊
ESAIM-MATHEMATICAL MODELLING AND NUMERICAL ANALYSIS
卷 55, 期 2, 页码 595-625出版社
EDP SCIENCES S A
DOI: 10.1051/m2an/2020079
关键词
Scott-Zhang operator; Besov space; multilevel decomposition; fractional Laplacian; preconditioning
资金
- Austrian Science Fund (FWF) through the research program Taming complexity in partial differential systems [SFB F65, P 28367-N35]
The article provides an endpoint stability result for Scott-Zhang type operators in Besov spaces, showing that these operators are bounded from H-3/2 into B-2,infinity(3/2) for globally continuous piecewise polynomials, and from H-1/2 into B-2,infinity(1/2) for element wise polynomials. An application of this result is a multilevel decomposition based on Scott-Zhang operators on a hierarchy of meshes generated by newest vertex bisection, with an exclusion of the endpoint case. Additionally, a local multilevel diagonal preconditioner for the fractional Laplacian on locally refined meshes with optimal eigenvalue bounds is presented.
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-2,infinity(3/2); for element wise polynomials these are bounded from H-1/2 into B-2,infinity(1/2). 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.
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