Details
| Originalsprache | Englisch |
|---|---|
| Seiten (von - bis) | 105-124 |
| Seitenumfang | 20 |
| Fachzeitschrift | Applied Numerical Mathematics |
| Jahrgang | 152 |
| Frühes Online-Datum | 21 Jan. 2020 |
| Publikationsstatus | Veröffentlicht - Juni 2020 |
Abstract
We consider the convergence of adaptive BEM for weakly-singular and hypersingular integral equations associated with the Laplacian and the Helmholtz operator in 2D and 3D. The local mesh-refinement is driven by some two-level error estimator. We show that the adaptive algorithm drives the underlying error estimates to zero. Moreover, we prove that the saturation assumption already implies linear convergence of the error with optimal algebraic rates.
ASJC Scopus Sachgebiete
- Mathematik (insg.)
- Numerische Mathematik
- Mathematik (insg.)
- Computational Mathematics
- Mathematik (insg.)
- Angewandte Mathematik
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in: Applied Numerical Mathematics, Jahrgang 152, 06.2020, S. 105-124.
Publikation: Beitrag in Fachzeitschrift › Artikel › Forschung › Peer-Review
}
TY - JOUR
T1 - The saturation assumption yields optimal convergence of two-level adaptive BEM
AU - Praetorius, Dirk
AU - Ruggeri, Michele
AU - Stephan, Ernst P.
N1 - Funding Information: The author DP acknowledges the support of the Austria Science Fund (FWF) through the research project Optimal adaptivity for BEM and FEM-BEM coupling (grant P27005) and the special research program (SFB) Taming complexity in partial differential systems (grant F65).
PY - 2020/6
Y1 - 2020/6
N2 - We consider the convergence of adaptive BEM for weakly-singular and hypersingular integral equations associated with the Laplacian and the Helmholtz operator in 2D and 3D. The local mesh-refinement is driven by some two-level error estimator. We show that the adaptive algorithm drives the underlying error estimates to zero. Moreover, we prove that the saturation assumption already implies linear convergence of the error with optimal algebraic rates.
AB - We consider the convergence of adaptive BEM for weakly-singular and hypersingular integral equations associated with the Laplacian and the Helmholtz operator in 2D and 3D. The local mesh-refinement is driven by some two-level error estimator. We show that the adaptive algorithm drives the underlying error estimates to zero. Moreover, we prove that the saturation assumption already implies linear convergence of the error with optimal algebraic rates.
KW - Adaptive methods
KW - Boundary element method
KW - Convergence
KW - Optimality
KW - Two-level error estimation
UR - http://www.scopus.com/inward/record.url?scp=85078412686&partnerID=8YFLogxK
U2 - 10.1016/j.apnum.2020.01.014
DO - 10.1016/j.apnum.2020.01.014
M3 - Article
AN - SCOPUS:85078412686
VL - 152
SP - 105
EP - 124
JO - Applied Numerical Mathematics
JF - Applied Numerical Mathematics
SN - 0168-9274
ER -