Hailong Guo

Deep Unfitted Nitsche Method for Elliptic Interface Problems

Hailong Guo, Xu Yang

Journal article  |  2022  |  COMMUNICATIONS IN COMPUTATIONAL PHYSICS

This paper proposes a deep unfitted Nitsche method for solving elliptic interface problems with high contrasts in high dimensions...

LOW ORDER MIXED FINITE ELEMENT APPROXIMATIONS OF THE MONGE-AMPÈRE EQUATION

J Adetola, B Ahounou, G Awanou, H Guo

Journal article  |  2022  |  International Journal of Numerical Analysis and Modeling

OPTIMAL MAXIMUM NORM ESTIMATES FOR VIRTUAL ELEMENT METHODS

Wen-ming He, Hailong Guo

Journal article  |  2022  |  SIAM JOURNAL ON NUMERICAL ANALYSIS

The maximum norm error estimations for virtual element methods are studied. To establish the error estimations, we prove higher lo..

Unfitted Nitsche's Method for Computing Wave Modes in Topological Materials

Hailong Guo, Xu Yang, Yi Zhu

Journal article  |  2021  |  JOURNAL OF SCIENTIFIC COMPUTING

In this paper, we propose an unfitted Nitsche’s method for computing wave modes in topological materials. The proposed method is b..

Unfitted Nitsche's method for computing band structures of phononic crystals with periodic inclusions

Hailong Guo, Xu Yang, Yi Zhu

Journal article  |  2021  |  COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING

In this paper, we propose an unfitted Nitsche's method to compute the band structures of phononic crystal with periodic inclusions..

Surface Crouzeix-Raviart element for the Laplace-Beltrami equation

Hailong Guo

Journal article  |  2020  |  NUMERISCHE MATHEMATIK

In this paper, we are concerned with the nonconforming finite element discretization of geometric partial differential equations. ..

PARAMETRIC POLYNOMIAL PRESERVING RECOVERY ON MANIFOLDS

Guozhi Dong, Hailong Guo

Journal article  |  2020  |  SIAM JOURNAL ON SCIENTIFIC COMPUTING

This paper investigates gradient recovery schemes for data defined on discretized manifolds. The proposed method, parametric polyn..

Superconvergent gradient recovery for virtual element methods

Hailong Guo, Cong Xie, Ren Zhao

Journal article  |  2019  |  MATHEMATICAL MODELS & METHODS IN APPLIED SCIENCES

Virtual element method is a new promising finite element method using general polygonal meshes. Its optimal a priori error estimat..

Hessian recovery based finite element methods for the Cahn-Hilliard equation

Minqiang Xu, Hailong Guo, Qingsong Zou

Journal article  |  2019  |  JOURNAL OF COMPUTATIONAL PHYSICS

In this paper, we propose several novel recovery based finite element methods for the 2D Cahn-Hilliard equation. One distinguishin..

Bloch theory-based gradient recovery method for computing topological edge modes in photonic graphene

Hailong Guo, Xu Yang, Yi Zhu

Journal article  |  2019  |  JOURNAL OF COMPUTATIONAL PHYSICS

Photonic graphene, a photonic crystal with honeycomb structures, has been intensively studied in both theoretical and applied fiel..