Summary.
We consider an indirect boundary integral equation formulation for the mixed Dirichlet-Neumann boundary value problem for the Laplace equation on a plane domain with a polygonal boundary. The resulting system of integral equations is solved by a collocation method which uses a mesh grading transformation and a cosine approximating space. The mesh grading transformation method yields fast convergence of the collocation solution by smoothing the singularities of the exact solution. A complete stability and solvability analysis of the transformed integral equations is given by use of a Mellin transform technique, in a setting in which each arc of the polygon has associated with it a periodic Sobolev space.
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Received April 15, 1995 / Revised version received April 10, 1996
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Elschner, J., Jeon, Y., Sloan, I. et al. The collocation method for mixed boundary value problems on domains with curved polygonal boundaries . Numer. Math. 76, 355–381 (1997). https://doi.org/10.1007/s002110050267
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DOI: https://doi.org/10.1007/s002110050267