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Laplace equation in a convex polygon: a numerical implementation of the weak formulation of the Fokas method

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In this talk I will describe a numerical implementation of the Fokas method to solving the Laplace equation in a convex polygon. This follows work by Fokas (2001, 2003) and Ashon (2012) which formulates a weak variational approach in the case of a convex polygon. This method uses strongly the analyticity of the Fourier Transform, and a powerful theorem by Paley and Wiener. The computational method uses a Galerkin approach with a natural sinc basis for the Paley-Wiener space. We discuss computational issues to this approach and possible resolutions relating to its implementation. The role of rigorous analysis cannot be underestimated in resolving these computational difficulties.

This talk is part of the Cambridge Analysts' Knowledge Exchange series.

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