论文标题
关于基于Voronoï
On pointwise error estimates for Voronoï-based finite volume methods for the Poisson equation on the sphere
论文作者
论文摘要
在本文中，我们给出了基于Voronoï的有限体积的估计值，该体积近似在球体的Voronoï-Delaunay分解上。这些估计是对泊松方程及其梯度的近似解的局部误差分析的基础。在这里，我们将基于Voronoï的有限体积方法视为有限元方法的扰动。最后，使用正则化绿色功能，我们以最大规律性要求得出了最大值的准最佳收敛顺序。数值示例表明，收敛至少与预期一样好。
In this paper, we give pointwise estimates of a Voronoï-based finite volume approximation of the Laplace-Beltrami operator on Voronoï-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 Voronoï-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.
