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math.NA2026
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…
math.NA2026
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…
math.NA2023
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…