S. Ferraz-Leite, D. Praetorius:

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

Computing,83(2008), 135 - 162.

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 $${\eta:=\Vert\phi_{h/2}-\phi_h\Vert}$$ to estimate the error $${\Vert\phi-\phi_h\Vert}$$ , where $${\phi_h}$$ is a Galerkin solution with respect to a mesh $${\mathcal{T}_h}$$ and $${\phi_{h/2}}$$ is a Galerkin solution with respect to the mesh $${\mathcal{T}_{h/2}}$$ obtained from a uniform refinement of $${\mathcal{T}_h}$$ . 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 η does not provide information for a local mesh-refinement. We consider Symm´s integral equation of the first kind, where the energy space is the negative-order Sobolev space $${\widetilde{H}^{-1/2^{\vphantom{H}}}(\Gamma)}$$ . Recent localization techniques allow to replace the energy norm in this case by some weighted L 2-norm. Then, this very basic error estimation strategy is also applicable to steer an h-adaptive algorithm. Numerical experiments in 2D and 3D show that the proposed method works well in practice. A short conclusion is concerned with other integral equations, e.g., the hypersingular case with energy space $${\widetilde{H}^{1/2}(\Gamma)}$$ and $${H^{1/2}_0(\Gamma)}$$ , respectively, or a transmission problem.

http://dx.doi.org/10.1007/s00607-008-0017-4

http://dx.doi.org/10.1007/s00607-008-0017-4

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