Discrete qualocation methods for logarithmic-kernel integral equations on a piecewise smooth boundary (Q1371971)

The paper studies the convergence of a qualocation method for Symm's integral equation on a closed polygonal curve. Using a special parametrization corresponding to mesh grading the equation is transformed to an integral equation with smoother solution. Discrete qualocation and a modification with substraction of singularities is applied to the transformed equation. The use of mesh-grading transformations together with a uniform mesh allows to analyse the principal term by Fourier methods and to study the corner effects by Mellin convolution arguments. Thus qualocation methods, previously analysed only for smooth curves, can be extended to curves with corners. The authors obtain optimal error estimates for the solution and for certain linear functionals.