The saturation assumption yields optimal convergence of two-level adaptive BEM

Dirk Praetorius; Michele Ruggeri; Ernst P. Stephan

doi:10.1016/j.apnum.2020.01.014

The saturation assumption yields optimal convergence of two-level adaptive BEM

Dirk Praetorius, Michele Ruggeri^*, Ernst P. Stephan

^*Corresponding author for this work

Mathematics And Statistics

Research output: Contribution to journal › Article › peer-review

3 Citations (Scopus)

18 Downloads (Pure)

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.

Original language	English
Pages (from-to)	105-124
Number of pages	20
Journal	Applied Numerical Mathematics
Volume	152
Early online date	20 Feb 2020
DOIs	https://doi.org/10.1016/j.apnum.2020.01.014
Publication status	Published - 30 Jun 2020

Funding

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 ). 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).

Keywords

adaptive methods
boundary element method
convergence
optimality
two-level error estimation

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10.1016/j.apnum.2020.01.014

Praetorius-etal-ANM-2021-The-saturation-assumption-yields-optimal-convergenceAccepted author manuscript, 991 KBLicence: CC BY-NC-ND 4.0

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title = "The saturation assumption yields optimal convergence of two-level adaptive BEM",

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.",

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author = "Dirk Praetorius and Michele Ruggeri and Stephan, \{Ernst P.\}",

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T1 - The saturation assumption yields optimal convergence of two-level adaptive BEM

AU - Praetorius, Dirk

AU - Ruggeri, Michele

AU - Stephan, Ernst P.

PY - 2020/6/30

Y1 - 2020/6/30

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

U2 - 10.1016/j.apnum.2020.01.014

DO - 10.1016/j.apnum.2020.01.014

M3 - Article

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VL - 152

SP - 105

EP - 124

JO - Applied Numerical Mathematics

JF - Applied Numerical Mathematics

ER -

The saturation assumption yields optimal convergence of two-level adaptive BEM

Abstract

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Keywords

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