On pointwise error estimates for Vorono\"i-based finite volume methods for the Poisson equation on the sphere
Numerical Analysis
2023-03-21 v2 Numerical Analysis
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.
Keywords
Cite
@article{arxiv.2206.03685,
title = {On pointwise error estimates for Vorono\"i-based finite volume methods for the Poisson equation on the sphere},
author = {Leonardo A. Poveda and Pedro Peixoto},
journal= {arXiv preprint arXiv:2206.03685},
year = {2023}
}