On pointwise error estimates for Voronoi-based finite volume methods for the Poisson equation on the sphere

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Author(s):	Poveda, Leonardo A. A. ; Peixoto, Pedro Total Authors: 2
Document type:	Journal article
Source:	ADVANCES IN COMPUTATIONAL MATHEMATICS; v. 49, n. 3, p. 37-pg., 2023-06-01.
Abstract
In this paper, we give pointwise estimates of a Voronoi-based finite volume approximation of the Laplace-Beltrami operator on Voronoi-Delaunay decompositions of the sphere. These estimates are the basis for local error analysis, in the maximum norm, of the approximate solution of the Poisson equation and its gradient. Here, we consider the Voronoi-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. (AU)

FAPESP's process:	21/06176-0 - Numerical methods for a new generation of weather and climate models
Grantee:	Pedro da Silva Peixoto
Support Opportunities:	Research Grants - Research Program on Global Climate Change - Young Investigators - Phase 2


FAPESP's process:	16/18445-7 - Numerical methods for the next generation weather and climate models
Grantee:	Pedro da Silva Peixoto
Support Opportunities:	Research Grants - Young Investigators Grants