31 citations · 188 across the 26 of their papers we have counts for
28 papers
A Gradient Recovery Method for Electron Magnetohydrodynamics with Fractional Dissipation
Hailong Guo, Ruimeng Hu, Qirui Peng +1
We propose and analyze a structure-preserving numerical method for the -dimensional (2.5D) electron magnetohydrodynamics system with fractional dissipation on the pe…
Polynomial preserving recovery for PHT-splines
Ying Cai, Falai Chen, Hailong Guo +2
We propose a polynomial preserving recovery method for PHT-splines within isogeometric analysis to obtain more accurate gradient approximations. The method fully exploits the local…
Recovery Techniques for Finite Element Methods
Hailong Guo, Zhimin Zhang
Post-processing techniques are essential tools for enhancing the accuracy of finite element approximations and achieving superconvergence. Among these, recovery techniques stand ou…
New interior penalty method for Monge-Ampère equations
Tianyang Chu, Hailong Guo, Zhimin Zhang
Monge-Ampère equation is a prototype second-order fully nonlinear partial differential equation. In this paper, we propose a new idea to design and analyze the interior penal…
Virtual Element Methods for HJB Equations with Cordes Coefficients
Ying Cai, Hailong Guo, Zhimin Zhang
In this paper, we propose and analyze both conforming and nonconforming virtual element methods (VEMs) for the fully nonlinear second-order elliptic Hamilton-Jacobi-Bellman (HJB) e…
Continuous Linear Finite Element Method for Biharmonic Problems on Surfaces
Ying Cai, Hailong Guo, Zhimin Zhang
This paper presents an innovative continuous linear finite element approach to effectively solve biharmonic problems on surfaces. The key idea behind this method lies in the strate…
Superconvergent postprocessing of interior penalty method
Ying Cai, Hailong Guo, Zhimin Zhang
This paper focuses on the superconvergence analysis of the Hessian recovery technique for the Interior Penalty Method (C0IP) in solving the biharmonic equation. We establish…
Unfitted finite element method for the quad-curl interface problem
Hailong Guo, Mingyan Zhang, Qian Zhang +1
In this paper, we introduce a novel unfitted finite element method to solve the quad-curl interface problem. We adapt Nitsche's method for curlcurl-conforming elements and double t…
Unfitted Spectral Element Method for interfacial models
Nicolas Gonzalez, Hailong Guo, Xu Yang
In this paper, we propose the unfitted spectral element method for solving elliptic interface and corresponding eigenvalue problems. The novelty of the proposed method lies in its…
Temporal Difference Learning for High-Dimensional PIDEs with Jumps
Liwei Lu, Hailong Guo, Xu Yang +1
In this paper, we propose a deep learning framework for solving high-dimensional partial integro-differential equations (PIDEs) based on the temporal difference learning. We introd…
Deep unfitted Nitsche method for elliptic interface problems
Hailong Guo, Xu Yang
This paper proposes a deep unfitted Nitsche method for computing elliptic interface problems with high contrasts in high dimensions. To capture discontinuities of the solution caus…
Optimal maximum norm estimates for virtual element methods
Wen-Ming He, Hailong Guo
The maximum norm error estimations for virtual element methods are studied. To establish the error estimations, we prove higher local regularity based on delicate analysis of Green…
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…
Unfitted Nitsche's method for computing band structures in phononic crystals with impurities
Hailong Guo, Xu Yang, Yi Zhu
In this paper, we propose an unfitted Nitsche's method to compute the band structures of phononic crystal with impurities of general geometry. The proposed method does not require…
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…
Unfitted Nitsche's method for computing wave modes in topological materials
Hailong Guo, Xu Yang, Yi Zhu
In this paper, we propose an unfitted Nitsche's method for computing wave modes in topological materials. The proposed method is based on Nitsche's technique to study the performan…
Surface Crouzeix-Raviart element for the Laplace-Beltrami equation
Hailong Guo
This paper is concerned with the nonconforming finite element discretization of geometric partial differential equations. In specific, we construct a surface Crouzeix-Raviart eleme…
Hessian recovery based finite element methods for the Cahn-Hilliard Equation
Minqiang Xu, Hailong Guo, Qingsong Zou
In this paper, we propose a novel recovery based finite element method for the Cahn-Hilliard equation. One distinguishing feature of the method is that we discretize the fourth-ord…
A linear finite element method for sixth order elliptic equations
Hailong Guo, Zhimin Zhang, Qingsong Zou
In this paper, we develop a straightforward linear finite element method for sixth-order elliptic equations. The basic idea is to use gradient recovery techniques to generate…
Superconvergent Gradient Recovery for Virtual Element Methods
Hailong Guo, Cong Xie, Ren Zhao
Virtual element methods is a new promising finite element methods using general polygonal meshes. Its optimal a priori error estimates are well established in the literature. In th…
Bloch theory-based gradient recovery method for computing topological edge modes in photonic graphene
Hailong Guo, Xu Yang, Yi Zhu
Photonic graphene, a photonic crystal with honeycomb structures, has been intensively studied in both theoretical and applied fields. Similar to graphene which admits Dirac Fermion…
Gradient recovery for elliptic interface problem: III. Nitsche's method
Hailong Guo, Xu Yang
This is the third paper on the study of gradient recovery for elliptic interface problem. In our previous works [H. Guo and X. Yang, 2016, arXiv:1607.05898 and {\it J. Comput. Phys…
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…
Superconvergence analysis of partially penalized immersed finite element method
Hailong Guo, Xu Yang, Zhimin Zhang
The contribution of this paper contains two parts: first, we prove a supercloseness result for the partially penalized immersed finite element (PPIFE) method in [T. Lin, Y. Lin, an…