4 papers
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…
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…