Green Function for a Two-Dimensional Discrete Laplace-Beltrami Operator
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Volodymyr Sushch
volodymyr.sushch@tu.koszalin.pl
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Abstract
We study a discrete model of the Laplacian in â„2 that preserves the geometric structure of the original continual object. This means that, speaking of a discrete model, we do not mean just the direct replacement of differential operators by difference ones but also a discrete analog of the Riemannian structure. We consider this structure on the appropriate combinatorial analog of differential forms. Self-adjointness and boundness for a discrete Laplacian are proved. We define the Green function for this operator and also derive an explicit formula of the one.
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Published
2008-07-01
How to Cite
[1]
V. Sushch, “Green Function for a Two-Dimensional Discrete Laplace-Beltrami Operator”, CUBO, vol. 10, no. 2, pp. 47–59, Jul. 2008.
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