Two discrete finite-difference Laplacians on H^2 are constructed, shown to be L2-stable and convergent to the continuous Laplace-Beltrami operator, with exponential decay matching the Poincaré inequality, and one geometry-tailored version outperforming the other.
Strichartz estimates in the hyperbolic space and global existence for the semilinear wave equation
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Discrete Laplacians on the hyperbolic space -- a comparative study
Two discrete finite-difference Laplacians on H^2 are constructed, shown to be L2-stable and convergent to the continuous Laplace-Beltrami operator, with exponential decay matching the Poincaré inequality, and one geometry-tailored version outperforming the other.