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arXiv · 2206.03685

On pointwise error estimates for Vorono\"i-based finite volume methods for the Poisson equation on the sphere

Leonardo A. Poveda·Pedro Peixoto
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Abstract

In this paper, we give pointwise estimates of a Vorono\"i-based finite volume approximation of the Laplace-Beltrami operator on Vorono\"i-Delaunay decompositions of the sphere. These estimates are the basis for a local error analysis, in the maximum norm, of the approximate solution of the Poisson equation and its gradient. Here, we consider the Vorono\"i-based finite volume method as a perturbation of the finite element method. Finally, using regularized Green's functions, we derive quasi-optimal convergence order in the maximum-norm with minimal regularity requirements. Numerical examples show that the convergence is at least as good as predicted.

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Leonardo A. Poveda, Pedro Peixoto. 2022-06-08. On pointwise error estimates for Vorono\"i-based finite volume methods for the Poisson equation on the sphere. https://arxiv.org/abs/2206.03685

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