Details
| Original language | English |
|---|---|
| Pages (from-to) | 603-621 |
| Number of pages | 19 |
| Journal | Computational Methods in Applied Mathematics |
| Volume | 23 |
| Issue number | 3 |
| Early online date | 14 Feb 2023 |
| Publication status | Published - 1 Jul 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.
Keywords
- Adaptive Methods, Finite Element Methods, Fractional Laplacian, Optimal Convergence, Two-Level Error Estimation
ASJC Scopus subject areas
- Mathematics(all)
- Numerical Analysis
- Mathematics(all)
- Computational Mathematics
- Mathematics(all)
- Applied Mathematics
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In: Computational Methods in Applied Mathematics, Vol. 23, No. 3, 01.07.2023, p. 603-621.
Research output: Contribution to journal › Article › Research › 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 -