A Unified Divergence Analysis on Projection Method for Symm's Integral Equation of the First Kind
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A large amount of literatures analyze (SIE) which concerns the construction of conformal mapping and boundary value problem of Laplace equation. However, there remains a long-term absence for a systematic divergence analysis. In this paper, we utilize [3, Theorem 2.2 (c)] to give a systematic divergence analysis for (SIE) with least squares, dual least squares, Babunov-Galerkin method in trigonometric basis. In particular, we show that the strong ellipticity estimate and Gärding inequality are also powerful in divergence analysis of Galerkin method on ill-posed integral equations.
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