4 papers
Stabilization-free virtual element methods based on finite element interpolation
Jikun Zhao, Wenhao Zhu, Bei Zhang +1
In this paper, we introduce a new framework for designing stabilization-free virtual element methods (VEMs) based on an finite element interpolation-based strategy, where we can si…
A Second-Order Maximum-Principle-Preserving Crouzeix-Raviart Finite Element Method for Time-dependent Transport Equation
Shipeng Mao, Mingyang Zhang
In this paper, we construct an explicit, second-order, and maximum-principle-preserving Crouzeix-Raviart (CR) finite element method for two-dimensional time-dependent transport equ…
MHDnet: Physics-preserving learning for solving magnetohydrodynamics problems
Xiaofei Guan, Boya Hu, Shipeng Mao +2
Designing efficient and high-accuracy numerical methods for complex dynamic incompressible magnetohydrodynamics (MHD) equations remains a challenging problem in various analysis an…
Approximate Acoustic Cloaking in Inhomogeneous Isotropic Space
Hongyu Liu
In this paper, we consider the approximate acoustic cloaking in inhomogeneous isotropic background space. By employing transformation media, together with the use of a sound-soft l…