25 citations · 47 across the 12 of their papers we have counts for
6 papers · 1 filter
Second-order flows for computing the ground states of rotating Bose-Einstein condensates
Haifan Chen, Guozhi Dong, Wei Liu +1
Second-order flows in this paper refer to some artificial evolutionary differential equations involving second-order time derivatives distinguished from gradient flows which are co…
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…
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…
Parametric Polynomial Preserving Recovery on Manifolds
Guozhi Dong, Hailong Guo
This paper investigates gradient recovery schemes for data defined on discretized manifolds. The proposed method, parametric polynomial preserving recovery (PPPR), does not require…
Nonlinear Flows for Displacement Correction and Applications in Tomography
Guozhi Dong, Otmar Scherzer
In this paper we derive nonlinear evolution equations associated with a class of non-convex energy functionals which can be used for correcting displacement errors in imaging data.…
Convergence of Tikhonov regularization for solving ill-posed operator equations with solutions defined on surfaces
Guozhi Dong, Bert Juettler, Otmar Scherzer +1
We study Tikhonov regularization for solving ill--posed operator equations where the solutions are functions defined on surfaces. One contribution of this paper is an error analysi…