3 papers
math.NA2026
A High-Order Surface Finite Element Method Based on Intersections with Background Tetrahedral Meshes
Zibo Zhao, Zuoqiang Shi
This paper develops a high-order surface finite element method for elliptic equations posed on a smooth closed surface implicitly defined as the zero level set of a function in thr…
math.NA2025
High-Order Quadrature for Implicitly Defined Surfaces and Regions
Zibo Zhao, Zuoqiang Shi
We propose a high-order quadrature method for integrating over curves, surfaces, and enclosed regions defined implicitly as zero level sets of smooth functions. The method combines…
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…