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Discrete qualocation methods for logarithmic-kernel integral equations on a piecewise smooth boundary |
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| Authors: | Jeon Y Sloan IH Stephan EP Elschner J |
| Institution: | 1.Department of Mathematics, Ajou University, Suwon, 441-749, Korea ;2.School of Mathematics, University of New South Wales, Sydney, NSW, 2052, Australia ;3.Institut für Angewandte Mathematik, Universität Hannover, Postfach 6009, D-30060, Hannover, Germany ;4.Weierstraß-Institut für Angewandte Analysis und Stochastik, Mohrenstraße, 39, D-10117, Berlin, Germany ; |
| Abstract: | We consider a fully discrete qualocation method for Symm’s integral equation. The method is that of Sloan and Burn (1992), 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, 1996). 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 (1995) and Elschner and Stephan (1996), to overcome the singular behavior of solutions at corners. This revised version was published online in August 2006 with corrections to the Cover Date. |
| Keywords: | discrete qualocation Symm’ s integral equation piecewise smooth boundary 65R20 65N38 |
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