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math.NA2023
Adaptive trajectories sampling for solving PDEs with deep learning methods
Xingyu Chen, Jianhuan Cen, Qingsong Zou
In this paper, we propose a new adaptive technique, named adaptive trajectories sampling (ATS), which is used to select training points for the numerical solution of partial differ…
math.NA2022
Two types of spectral volume methods for 1-D linear hyperbolic equations with degenerate variable coefficients
Minqiang Xu, Yanting yuan, Waixiang Cao +1
In this paper, we analyze two classes of spectral volume (SV) methods for one-dimensional hyperbolic equations with degenerate variable coefficients. The two classes of SV methods…
math.NA2022
A Linear Finite Element Method for a Second Order Elliptic Equation in Non-Divergence Form with Cordes Coefficients
Minqiang Xu, Runchang Lin, Qingsong Zou
In this paper, we develop a gradient recovery based linear (GRBL) finite element method (FEM) and a Hessian recovery based linear (HRBL) FEM for second order elliptic equations in…