Geodesic
A Block Method for Solving the Laplace Equation in a Disk with a Hole That Has Cuts
Trudy Matematicheskogo Instituta imeni V.A. Steklova, Studies on function theory and differential equations, Tome 248 (2005), pp. 86-93 Cet article a éte moissonné depuis la source Math-Net.Ru

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A numerical–analytic block method proposed by the author is applied to construct an approximate solution to the Dirichlet problem for the Laplace equation in a disk with an elliptic hole that has two cuts. The construction employs two blocks–rings and an elementary conformal mapping. It is shown that the approximate solution converges, in the uniform metric, exponentially with respect to the order of a rapidly solvable system of linear algebraic equations. 
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     title = {A~Block {Method} for {Solving} the {Laplace} {Equation} in {a~Disk} with {a~Hole} {That} {Has} {Cuts}},
     journal = {Trudy Matematicheskogo Instituta imeni V.A. Steklova},
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E. A. Volkov. A Block Method for Solving the Laplace Equation in a Disk with a Hole That Has Cuts. Trudy Matematicheskogo Instituta imeni V.A. Steklova, Studies on function theory and differential equations, Tome 248 (2005), pp. 86-93. http://geodesic.mathdoc.fr/item/TM_2005_248_a8/

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[4] Volkov E.A., Block method for solving the Laplace equation and for constructing conformal mappings, CRC Press, Boca Raton (Florida), 1994 | MR | Zbl