3 papers
math.NA2025
Discontinuous Galerkin methods for the Laplace-Beltrami operator on point cloud
Guozhi Dong, Hailong Guo, Zuoqiang Shi
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…
math.NA2025
Superconvergence of differential structure for finite element methods on perturbed surface meshes
Guozhi Dong, Hailong Guo, Ting Guo
Superconvergence of differential structure on discretized surfaces is studied in this paper. The newly introduced geometric supercloseness provides us with a fundamental tool to pr…
math.AP2025
A class of second-order geometric quasilinear hyperbolic PDEs and their application in imaging science
Guozhi Dong, Michael Hintermüller, Ye Zhang
Motivated by important applications in image processing, we study a class of second-order geometric quasilinear hyperbolic partial differential equations (PDEs). This is inspired b…