PreprintNumerical solution of the 2D Poisson equation on an irregular domain with Robin boundary conditionsZ. Jomaa and C. MacaskillAbstractWe describe a 2D finite difference algorithm for inverting the Poisson equation on an irregularly shaped domain, with mixed boundary conditions, with the domain embedded in a rectangular Cartesian grid. We give both linear and quadratic boundary treatments and derive 1D error expressions for both cases. The linear approach uses a 5point formulation and is firstorder accurate while the quadratic treatment uses a 9point stencil and is secondorder accurate. The key aspect of the quadratic treatment is the use of a suitably chosen directional derivative to find the second order accurate approximation to the normal derivative at the boundary. Keywords: Poisson equation, Robin boundary conditions, linear, quadratic, directional derivative.AMS Subject Classification: Primary Numerical; secondary analysis.
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