S. Ferraz-Leite, D. Praetorius:

"Adaptive boundary element methods based on accurate a posteriori error estimation";

in: "ASC Report 23/2008", issued by: Institute for Analysis and Scientific Computing; Vienna University of Technology, Wien, 2008, ISBN: 978-3-902627-01-8.

The boundary element method is one strategy to solve partial

differential equations of elliptic type. As model problem, we consider

the computation of the charge density \phi and the capacitance C of a

thin electrified plate. We introduce an intelligent algorithm based on

certain error estimators. The mesh-refinement is steered automatically

in the sense that the mesh is locally refined, where the error

appears to be large. Numerical experiments show that the new method

reveals the optimal order of convergence and is therefore

significantly faster than a standard uniform approach. All

mathematical results are valid in a quite general framework and thus

apply to a large problem class, including, e.g., the Laplace problem,

the Stokes system, and the Lame equation.

http://www.asc.tuwien.ac.at/preprint/2008/asc23x2008.pdf

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