Discrete qualocation methods for logarithmic-kernel integral equations on a piecewise smooth boundary
- Elschner, Johannes
- Jeon, Youngmok
- Sloan, Ian H.
- Stephan, Ernst P.
2010 Mathematics Subject Classification
- 65R20 65N38 45E10 65R30
- discrete qualocation, Symm´s integral equation, piecewise smooth boundary, graded mesh, logarithmic-kernel integral equations, substraction of singularities, Fourier methods, Mellin convolution, error estimates
We consider a fully discrete qualocation method for Symm's integral equation. The method is that of Sloan and Burn , for which a complete analysis is available in the case of smooth curves. The convergence for smooth curves can be improved by a subtraction of singularity (Jeon and Kimn ). In this paper we extend these results for smooth boundaries to polygonal boundaries. The analysis uses a mesh grading transformation method for Symm's integral equation, as in Elschner and Graham  and Elschner and Stephan , to overcome the singular behavior of solutions at corners.
- Adv. Comput. Math., 7 (1997), pp. 547-571