23 citations · 63 across the 11 of their papers we have counts for
11 papers
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…
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…
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…
Hessian recovery based finite element methods for the Cahn-Hilliard Equation
Minqiang Xu, Hailong Guo, Qingsong Zou
In this paper, we propose a novel recovery based finite element method for the Cahn-Hilliard equation. One distinguishing feature of the method is that we discretize the fourth-ord…
A linear finite element method for sixth order elliptic equations
Hailong Guo, Zhimin Zhang, Qingsong Zou
In this paper, we develop a straightforward linear finite element method for sixth-order elliptic equations. The basic idea is to use gradient recovery techniques to generate…
A Conservative Flux Optimization Finite Element Method for Convection-Diffusion Equations
Yujie Liu, Junping Wang, Qingsong Zou
This article presents a new finite element method for convection-diffusion equations by enhancing the continuous finite element space with a flux space for flux approximations that…
Superconvergence of immersed finite volume methods for one-dimensional interface problems
Waixiang Cao, Xu Zhang, Zhimin Zhang +1
In this paper, we introduce a class of high order immersed finite volume methods (IFVM) for one-dimensional interface problems. We show the optimal convergence of IFVM in H1 and L2…
Superconvergence of Discontinuous Galerkin method for linear hyperbolic equations
Cao Waixiang, Zhang Zhimin, Zou Qingsong
In this paper, we study superconvergence properties of the discontinuous Galerkin (DG) method for one-dimensional linear hyperbolic equation when upwind fluxes are used. We prove,…
Any order superconvergence finite volume schemes for 1D general elliptic equations
Waixiang Cao, Zhimin Zhang, Qingsong Zou
We present and analyze a finite volume scheme of arbitrary order for elliptic equations in the one-dimensional setting. In this scheme, the control volumes are constructed by using…
Finite volume schemes of any order on rectangular meshes
Zhimin Zhang, Qingsong Zou
In this paper, we analyze vertex-centered finite volume method (FVM) of any order for elliptic equations on rectangular meshes. The novelty is a unified proof of the inf-sup condit…
Flux-conserving finite element methods
Shangyou Zhang, Zhimin Zhang, Qingsong Zou
We analyze the flux conservation property of the finite element method. It is shown that the finite element solution does approximate the flux locally in the optimal order, i.e., t…