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

被引:0
作者
Poveda, Leonardo A. A. [1 ]
Peixoto, Pedro [2 ]
机构
[1] Chinese Univ Hong Kong, Dept Math, Shatin, Hong Kong, Peoples R China
[2] Univ Sao Paulo, Inst Matemat & Estat, Sao Paulo, Brazil
基金
巴西圣保罗研究基金会;
关键词
Laplace-Beltrami operator; Poisson equation; Spherical icosahedral grids; Finite volume method; a priori error estimates; Pointwise estimates; Uniform error estimates; SHALLOW-WATER EQUATIONS; BAROTROPIC VORTICITY EQUATION; MAXIMUM-NORM STABILITY; ELEMENT-METHOD; NUMERICAL-INTEGRATION; ELLIPTIC PROBLEMS; SUPERCONVERGENCE; SURFACE; MESHES; DISCRETIZATION;
D O I
10.1007/s10444-023-10041-3
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
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.
引用
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页数:37
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