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arXiv · 2012.15433

Discontinuous Galerkin methods for the Laplace-Beltrami operator on point cloud

Guozhi Dong·Hailong Guo·Zuoqiang Shi
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Abstract

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.

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Guozhi Dong, Hailong Guo, Zuoqiang Shi. 2020-12-31. Discontinuous Galerkin methods for the Laplace-Beltrami operator on point cloud. https://arxiv.org/abs/2012.15433

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