Summary
For three-dimensional domains with piecewise Lyapounov boundaries having corners and edges one can find simple corner points where the classical assumptions for the validity of the Fredholm-Radon boundary integral equation method with continuous charges are violated. As a consequence, in this case the convergence of the panel method was not justified either. However, the use of a suitable weighted maximum norm allows the justification of the method and the convergence for rectangular domains which violate the previous assumption. Here we give a survey on these relations between geometry, solvability of the integral equations and the convergence of the panel method by introducing a more general concept for the Fredholm radius. For general domains, however, it is still open whether corresponding weighted norms can be found.
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Kral, J., Wendland, W. (1988). On the Applicability of the Fredholm-Radon Method in Potential Theory and the Panel Method. In: Ballmann, J., Eppler, R., Hackbusch, W. (eds) Panel Methods in Fluid Mechanics with Emphasis on Aerodynamics. Notes on Numerical Fluid Mechanics, vol 21. Vieweg+Teubner Verlag, Wiesbaden. https://doi.org/10.1007/978-3-663-13997-3_10
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DOI: https://doi.org/10.1007/978-3-663-13997-3_10
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