Convergence of the point integral method for Laplace–Beltrami equation on point cloud

被引：0
作者：
Zuoqiang Shi
Jian Sun
机构：
[1] Tsinghua University,Yau Mathematical Sciences Center
来源：
Research in the Mathematical Sciences | / 4卷
关键词：
Laplace–Beltrami operator; Neumann boundary; Point cloud; Point integral method; Convergence analysis; 65N12; 65N25; 65N75;
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学科分类号：
摘要：
The Laplace–Beltrami operator, a fundamental object associated with Riemannian manifolds, encodes all intrinsic geometry of manifolds and has many desirable properties. Recently, we proposed the point integral method (PIM), a novel numerical method for discretizing the Laplace–Beltrami operator on point clouds (Li et al. in Commun Comput Phys 22(1):228–258, 2017). In this paper, we analyze the convergence of PIM for Poisson equation with Neumann boundary condition on submanifolds that are isometrically embedded in Euclidean spaces.
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