Abstract.
Convergence results for discrete solutions of Dirichlet problems for Poisson equations are obtained, where discrete solutions are constructed for triangular grids using finite volumes with sides perpendicular to, but not necessarily bisecting, corresponding edges in underlying triangulations. A method, based on properties of circle packings, is described for generating triangular meshes and associated volumes. Also, the approximation of exit probabilities of the Brownian motion by exit probabilities of random walks on circle packings is discussed.
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Received July 24, 1997, and in revised form November 8, 1998.
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Dubejko, T. Discrete Solutions of Dirichlet Problems, Finite Volumes, and Circle Packings . Discrete Comput Geom 22, 19–39 (1999). https://doi.org/10.1007/PL00009447
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DOI: https://doi.org/10.1007/PL00009447