Details
| Originalsprache | Englisch |
|---|---|
| Seiten (von - bis) | 603-621 |
| Seitenumfang | 19 |
| Fachzeitschrift | Computational Methods in Applied Mathematics |
| Jahrgang | 23 |
| Ausgabenummer | 3 |
| Frühes Online-Datum | 14 Feb. 2023 |
| Publikationsstatus | Veröffentlicht - 1 Juli 2023 |
Abstract
For the singular integral definition of the fractional Laplacian, we consider an adaptive finite element method steered by two-level error indicators. For this algorithm, we show linear convergence in two and three space dimensions as well as convergence of the algorithm with optimal algebraic rates in 2D, when newest vertex bisection is employed for mesh refinement. A key step hereby is an equivalence of the nodal and Scott-Zhang interpolation operators in certain weighted L2-norms.
ASJC Scopus Sachgebiete
- Mathematik (insg.)
- Numerische Mathematik
- Mathematik (insg.)
- Computational Mathematics
- Mathematik (insg.)
- Angewandte Mathematik
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in: Computational Methods in Applied Mathematics, Jahrgang 23, Nr. 3, 01.07.2023, S. 603-621.
Publikation: Beitrag in Fachzeitschrift › Artikel › Forschung › Peer-Review
}
TY - JOUR
T1 - Two-Level Error Estimation for the Integral Fractional Laplacian
AU - Faustmann, Markus
AU - Stephan, Ernst P.
AU - Wörgötter, David
PY - 2023/7/1
Y1 - 2023/7/1
N2 - For the singular integral definition of the fractional Laplacian, we consider an adaptive finite element method steered by two-level error indicators. For this algorithm, we show linear convergence in two and three space dimensions as well as convergence of the algorithm with optimal algebraic rates in 2D, when newest vertex bisection is employed for mesh refinement. A key step hereby is an equivalence of the nodal and Scott-Zhang interpolation operators in certain weighted L2-norms.
AB - For the singular integral definition of the fractional Laplacian, we consider an adaptive finite element method steered by two-level error indicators. For this algorithm, we show linear convergence in two and three space dimensions as well as convergence of the algorithm with optimal algebraic rates in 2D, when newest vertex bisection is employed for mesh refinement. A key step hereby is an equivalence of the nodal and Scott-Zhang interpolation operators in certain weighted L2-norms.
KW - Adaptive Methods
KW - Finite Element Methods
KW - Fractional Laplacian
KW - Optimal Convergence
KW - Two-Level Error Estimation
UR - http://www.scopus.com/inward/record.url?scp=85148670449&partnerID=8YFLogxK
U2 - 10.48550/arXiv.2209.13366
DO - 10.48550/arXiv.2209.13366
M3 - Article
AN - SCOPUS:85148670449
VL - 23
SP - 603
EP - 621
JO - Computational Methods in Applied Mathematics
JF - Computational Methods in Applied Mathematics
SN - 1609-4840
IS - 3
ER -