45 citations · 48 across the 5 of their papers we have counts for
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Fractional-order dependent Radial basis functions meshless methods for the integral fractional Laplacian
Zhaopeng Hao, Zhiqiang Cai, Zhongqiang Zhang
We study the numerical evaluation of the integral fractional Laplacian and its application in solving fractional diffusion equations. We derive a pseudo-spectral formula for the in…
Hybrid A Posteriori Error Estimators for Conforming Finite Element Approximations to Stationary Convection-Diffusion-Reaction equations
Difeng Cai, Zhiqiang Cai
We consider the a posteriori error estimation for convection-diffusion-reaction equations in both diffusion-dominated and convection/reaction-dominated regimes. We present an expli…
Adaptive Two-Layer ReLU Neural Network: II. Ritz Approximation to Elliptic PDEs
Min Liu, Zhiqiang Cai
In this paper, we study adaptive neuron enhancement (ANE) method for solving self-adjoint second-order elliptic partial differential equations (PDEs). The ANE method is a self-adap…
Least-Squares ReLU Neural Network (LSNN) Method For Linear Advection-Reaction Equation
Zhiqiang Cai, Jingshuang Chen, Min Liu
This paper studies least-squares ReLU neural network method for solving the linear advection-reaction problem with discontinuous solution. The method is a discretization of an equi…
Generalized Prager-Synge Inequality and Equilibrated Error Estimators for Discontinuous Elements
Cuiyu He, Zhiqiang Cai, Shun Zhang
The well-known Prager-Synge identity is valid in and serves as a foundation for developing equilibrated a posteriori error estimators for continuous elements. In this pape…