7 papers
Sparsely connected rank-inspired neural network
Yunqing Huang, Wu Su, Nianyu Yi +1
We propose a Sparsely Connected Rank-Inspired Neural Network (SCRINN) for function approximation and the numerical solution of partial differential equations (PDEs). By introducing…
A linear, fully decoupled, and unconditionally energy-stable SAV-FEM for the Cahn--Hilliard--Navier--Stokes model
Jinting Yang, Nianyu Yi, Peimeng Yin
In this paper, we develop a linear, fully decoupled, and unconditionally energy-stable fully discrete finite element scheme for the Cahn--Hilliard--Navier--Stokes (CHNS) system by…
Towards finite element methods for fourth-order elliptic equation. Part I: general boundary conditions
Xihao Zhang, Hengguang Li, Nianyu Yi +1
This paper is part of a series developing finite element methods for fourth-order elliptic equations on polygonal domains. Here, we investigate how boundary conditions influe…
Enhanced gradient recovery-based a posteriori error estimator and adaptive finite element method for elliptic equations
Ying Liu, Jingjing Xiao, Nianyu Yi +1
Recovery type a posteriori error estimators are popular, particularly in the engineering community, for their computationally inexpensive, easy to implement, and generally asymptot…
High Accuracy Techniques Based Adaptive Finite Element Methods for Elliptic PDEs
Jingjing Xiao, Ying Liu, Nianyu Yi
This paper aims to develop an efficient adaptive finite element method for the second-order elliptic problem. Although the theory for adaptive finite element methods based on resid…
Neural network-enhanced -adaptive finite element algorithm for parabolic equations
Jiaxiong Hao, Yunqing Huang, Nianyu Yi +1
In this paper, we propose a novel -adaptive finite element method, enhanced by neural networks, for parabolic equations. The main challenge of the conventional -adaptive fin…
A second-order dynamical low-rank mass-lumped finite element method for the Allen-Cahn equation
Jun Yang, Nianyu Yi, Peimeng Yin
In this paper, we propose a novel second-order dynamical low-rank mass-lumped finite element method for solving the Allen-Cahn (AC) equation, a semilinear parabolic partial differe…