Details
| Original language | English |
|---|---|
| Pages (from-to) | 595-625 |
| Number of pages | 31 |
| Journal | ESAIM: Mathematical Modelling and Numerical Analysis |
| Volume | 55 |
| Issue number | 2 |
| Publication status | Published - 1 Apr 2021 |
| Externally published | Yes |
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.
Keywords
- Besov space, Fractional Laplacian, Multilevel decomposition, Preconditioning, Scott-Zhang operator
ASJC Scopus subject areas
- Mathematics(all)
- General Mathematics
- Mathematics(all)
- Computational Mathematics
- Mathematics(all)
- Analysis
- Mathematics(all)
- Applied Mathematics
- Mathematics(all)
- Numerical Analysis
- Mathematics(all)
- Modelling and Simulation
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In: ESAIM: Mathematical Modelling and Numerical Analysis, Vol. 55, No. 2, 01.04.2021, p. 595-625.
Research output: Contribution to journal › Article › Research › 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 -