S. Ferraz-Leite, D. Praetorius:

"Simple A Posteriori Error Estimators for the h-Version of the Boundary Element Method";

in: "ASC Report 01/2007", issued by: Institute for Analysis and Scientific Computing; Vienna University of Technology, Wien, 2007, ISBN: 978-3-902627-00-1.

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.

http://www.asc.tuwien.ac.at/preprint/2007/asc01x2007.pdf

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