Geodesic
Grid Approximation of the First Derivatives of the Solution to the Dirichlet Problem for the Laplace Equation on a~Polygon
Trudy Matematicheskogo Instituta imeni V.A. Steklova, Function spaces, approximation theory, and nonlinear analysis, Tome 255 (2006), pp. 99-115

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Using the method of composite square and polar grids, we construct approximations of the first derivatives of the solution to the Dirichlet problem for the Laplace equation on a polygon and find error estimates for such approximations. 
@article{TM_2006_255_a7,
     author = {E. A. Volkov},
     title = {Grid {Approximation} of the {First} {Derivatives} of the {Solution} to the {Dirichlet} {Problem} for the {Laplace} {Equation} on {a~Polygon}},
     journal = {Trudy Matematicheskogo Instituta imeni V.A. Steklova},
     pages = {99--115},
     publisher = {mathdoc},
     volume = {255},
     year = {2006},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TM_2006_255_a7/}
}
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E. A. Volkov. Grid Approximation of the First Derivatives of the Solution to the Dirichlet Problem for the Laplace Equation on a~Polygon. Trudy Matematicheskogo Instituta imeni V.A. Steklova, Function spaces, approximation theory, and nonlinear analysis, Tome 255 (2006), pp. 99-115. http://geodesic.mathdoc.fr/item/TM_2006_255_a7/