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On the Characterization of Self-Regularization Properties of a Fully Discrete Projection Method for Symm's Integral Equation

The influence of small perturbations in the kernel and the righthand side of Symm’s boundary integral equation, considered in an ill-posed setting, is analyzed. We propose a modification of a fully discrete projection method which is more economical in the sense of complexity and allows one to obtain the optimal order of accuracy in the power scale with respect to the level of the noise in the kernel or in the parametric representation of the boundary.