Buchbeiträge:
S. Ferraz-Leite, D. Praetorius:
"Simple A Posteriori Error Estimators for the h-Version of the Boundary Element Method";
in: "ASC Report 01/2007",
herausgegeben von: Institute for Analysis and Scientific Computing;
Vienna University of Technology,
Wien,
2007,
ISBN: 978-3-902627-00-1.
Kurzfassung englisch:
The h-h/2-strategy is one well-known technique for the
a posteriori error estimation for Galerkin discretizations
of energy minimization problems. One considers
\eta_H:=\norm{\phi_h-\phi_{h/2}}
to estimate the error
\norm{\phi-\phi_h},
where \phi_h is a Galerkin solution with respect to a mesh
T_h and phi_{h/2} is a Galerkin solution with respect to the
mesh T_{h/2} obtained from a uniform refinement of T_h.
This error estimator is always efficient and observed to be
also reliable in practice. However, for boundary element
methods, the energy norm is non-local and thus the error
estimator \eta_H does not provide information for a local
mesh-refinement. Recent localization techniques allow to replace
the energy norm in this case by weighted L^2-norms resp.
H^1-seminorms. Therefore, this very basic error estimation
strategy is also applicable to steer an $h$-adaptive algorithm
for the boundary element method. Numerical experiments in 2D
and 3D show that the proposed method works well in practice.
As model examples serve the elliptic first-kind integral
equations with weakly singular and hypersingular integral
kernel.
Elektronische Version der Publikation:
http://www.asc.tuwien.ac.at/preprint/2007/asc01x2007.pdf
Erstellt aus der Publikationsdatenbank der Technischen Universität Wien.