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    On the Numerical Solution of the Laplace Equation with Complete and Incomplete Cauchy Data Using Integral Equations

    Christina Babenko1, Roman Chapko2, B. Tomas Johansson3

    CMES-Computer Modeling in Engineering & Sciences, Vol.101, No.5, pp. 299-317, 2014, DOI:10.3970/cmes.2014.101.299

    Abstract We consider the numerical solution of the Laplace equations in planar bounded domains with corners for two types of boundary conditions. The first one is the mixed boundary value problem (Dirichlet-Neumann), which is reduced, via a single-layer potential ansatz, to a system of well-posed boundary integral equations. The second one is the Cauchy problem having Dirichlet and Neumann data given on a part of the boundary of the solution domain. This problem is similarly transformed into a system of ill-posed boundary integral equations. For both systems, to numerically solve them, a mesh grading transformation is employed together with trigonometric quadrature… More >

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