Details
| Originalsprache | Englisch |
|---|---|
| Seiten (von - bis) | 595-625 |
| Seitenumfang | 31 |
| Fachzeitschrift | ESAIM: Mathematical Modelling and Numerical Analysis |
| Jahrgang | 55 |
| Ausgabenummer | 2 |
| Publikationsstatus | Veröffentlicht - 1 Apr. 2021 |
| Extern publiziert | Ja |
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 B3/22,∞; for element wise polynomials these are bounded from H1/2 into B1/22,∞. 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.
ASJC Scopus Sachgebiete
- Mathematik (insg.)
- Allgemeine Mathematik
- Mathematik (insg.)
- Computational Mathematics
- Mathematik (insg.)
- Analysis
- Mathematik (insg.)
- Angewandte Mathematik
- Mathematik (insg.)
- Numerische Mathematik
- Mathematik (insg.)
- Modellierung und Simulation
Zitieren
- Standard
- Harvard
- Apa
- Vancouver
- BibTex
- RIS
in: ESAIM: Mathematical Modelling and Numerical Analysis, Jahrgang 55, Nr. 2, 01.04.2021, S. 595-625.
Publikation: Beitrag in Fachzeitschrift › Artikel › Forschung › Peer-Review
}
TY - JOUR
T1 - On the stability of Scott-Zhang type operators and application to multilevel preconditioning in fractional diffusion
AU - Faustmann, Markus
AU - Melenk, Jens Markus
AU - Parvizi, Maryam
N1 - Funding information:. Financial support by the Austrian Science Fund (FWF) through the research program “Taming complexity in partial differential systems” (grant SFB F65) for JMM and through grant P 28367-N35 for JMM and MP is gratefully acknowledged.
PY - 2021/4/1
Y1 - 2021/4/1
N2 - 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 B3/22,∞; for element wise polynomials these are bounded from H1/2 into B1/22,∞. 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.
AB - 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 B3/22,∞; for element wise polynomials these are bounded from H1/2 into B1/22,∞. 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.
KW - Besov space
KW - Fractional Laplacian
KW - Multilevel decomposition
KW - Preconditioning
KW - Scott-Zhang operator
UR - http://www.scopus.com/inward/record.url?scp=85103742362&partnerID=8YFLogxK
U2 - 10.1051/m2an/2020079
DO - 10.1051/m2an/2020079
M3 - Article
VL - 55
SP - 595
EP - 625
JO - ESAIM: Mathematical Modelling and Numerical Analysis
JF - ESAIM: Mathematical Modelling and Numerical Analysis
SN - 0399-0516
IS - 2
ER -