论文标题
Laplace-Beltrami操作员的不连续的Galerkin方法在点云上
Discontinuous Galerkin methods for the Laplace-Beltrami operator on point cloud
论文作者
论文摘要
本文致力于开发用于解决分散点云上偏微分方程的高阶方法的数值分析。我们通过估计Riemann度量张量近似的误差来构建一个新颖的几何误差分析框架。创新的框架是分析可能不连续几何形状上应用于Laplace-Beltrami操作员的不连续的Galerkin方法的基本工具。我们提供了从点云重建的片状表面上的数值示例，以支持我们的理论发现。
This paper is dedicated to the development of numerical analysis for high-order methods solving partial differential equations on scattered point clouds. We build a novel geometric error analysis framework by estimating the error in the approximation of the Riemann metric tensor. The innovative framework serves as a fundamental tool for analyzing discontinuous Galerkin methods applied to the Laplace-Beltrami operator on possibly discontinuous geometry. We provide numerical examples on patchy surfaces reconstructed from point clouds to support our theoretical findings.
