WIAS Preprint No. 184, (1995)

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



Authors

  • Elschner, Johannes
  • Jeon, Youngmok
  • Sloan, Ian H.
  • Stephan, Ernst P.

2010 Mathematics Subject Classification

  • 65R20 65N38 45E10 65R30

Keywords

  • discrete qualocation, Symm´s integral equation, piecewise smooth boundary, graded mesh, logarithmic-kernel integral equations, substraction of singularities, Fourier methods, Mellin convolution, error estimates

Abstract

We consider a fully discrete qualocation method for Symm's integral equation. The method is that of Sloan and Burn [14], 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 [10]). 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 [4] and Elschner and Stephan [7], to overcome the singular behavior of solutions at corners.

Appeared in

  • Adv. Comput. Math., 7 (1997), pp. 547-571

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