Zhiqiang Cai - RankMe

72 papers Journal 72

Year	Rank	Type	Title / Venue / Authors
2026	J	`jnl`	Convergence Analysis of Block Newton Methods for 1D Shallow Neural Network Approximation. CoRR Zhiqiang Cai, Anastassia Doktorova, Robert D. Falgout, César Herrera
2025	J	`jnl`	Dual Neural Network (DuNN) method for elliptic partial differential equations and systems. J. Comput. Appl. Math. Min Liu, Zhiqiang Cai, Karthik Ramani
2025	J	`jnl`	Hybrid a posteriori error estimators for conforming finite element approximations to stationary convection-diffusion-reaction equations. Numerische Mathematik Difeng Cai, Zhiqiang Cai
2024	J	`jnl`	Fast Iterative Solver For Neural Network Method: I. 1D Diffusion Problems. CoRR Zhiqiang Cai, Anastassia Doktorova, Robert D. Falgout, César Herrera
2024	J	`jnl`	Fast Iterative Solver For Neural Network Method: II. 1D Diffusion-Reaction Problems And Data Fitting. CoRR Zhiqiang Cai, Anastassia Doktorova, Robert D. Falgout, César Herrera
2024	J	`jnl`	Fractional-order dependent Radial basis functions meshless methods for the integral fractional Laplacian. CoRR Zhaopeng Hao, Zhiqiang Cai, Zhongqiang Zhang
2024	J	`jnl`	Least-Squares Neural Network (LSNN) Method for Linear Advection-Reaction Equation: Discontinuity Interface. SIAM J. Sci. Comput. Zhiqiang Cai, Junpyo Choi, Min Liu
2024	J	`jnl`	ReLU neural network approximation to piecewise constant functions. CoRR Zhiqiang Cai, Junpyo Choi, Min Liu
2023	J	`jnl`	Adaptive Least-Squares Methods for Convection-Dominated Diffusion-Reaction Problems. CoRR Zhiqiang Cai, Binghe Chen, Jing Yang
2023	J	`jnl`	Deep Ritz Method with Adaptive Quadrature for Linear Elasticity. CoRR Min Liu, Zhiqiang Cai, Karthik Ramani
2023	J	`jnl`	Least-Squares Neural Network (LSNN) Method For Linear Advection-Reaction Equation: Non-constant Jumps. CoRR Zhiqiang Cai, Junpyo Choi, Min Liu
2023	J	`jnl`	Least-Squares Neural Network (LSNN) Method for Linear Advection-Reaction Equation: General Discontinuous Interface. CoRR Zhiqiang Cai, Junpyo Choi, Min Liu
2023	J	`jnl`	Least-squares neural network (LSNN) method for scalar nonlinear hyperbolic conservation laws: Discrete divergence operator. J. Comput. Appl. Math. Zhiqiang Cai, Jingshuang Chen, Min Liu
2023	J	`jnl`	Optimal error estimate of discontinuous Galerkin methods for advection-diffusion-reaction problems with low regularity. Comput. Math. Appl. Zhiqiang Cai, Jing Yang
2022	J	`jnl`	Adaptive two-layer ReLU neural network: I. Best least-squares approximation. Comput. Math. Appl. Min Liu, Zhiqiang Cai, Jingshuang Chen
2022	J	`jnl`	Adaptive two-layer ReLU neural network: II. Ritz approximation to elliptic PDEs. Comput. Math. Appl. Min Liu, Zhiqiang Cai
2022	J	`jnl`	Self-adaptive deep neural network: Numerical approximation to functions and PDEs. J. Comput. Phys. Zhiqiang Cai, Jingshuang Chen, Min Liu
2021	J	`jnl`	Adaptive Finite Element Method for Dirichlet Boundary Control of Elliptic Partial Differential Equations. J. Sci. Comput. Shaohong Du, Zhiqiang Cai
2021	J	`jnl`	Adaptive Two-Layer ReLU Neural Network: I. Best Least-squares Approximation. CoRR Min Liu, Zhiqiang Cai, Jingshuang Chen
2021	J	`jnl`	Adaptive Two-Layer ReLU Neural Network: II. Ritz Approximation to Elliptic PDEs. CoRR Min Liu, Zhiqiang Cai
2021	J	`jnl`	Finite Volume Least-Squares Neural Network (FV-LSNN) Method for Scalar Nonlinear Hyperbolic Conservation Laws. CoRR Zhiqiang Cai, Jingshuang Chen, Min Liu
2021	J	`jnl`	Generalized Prager-Synge identity and robust equilibrated error estimators for discontinuous elements. J. Comput. Appl. Math. Zhiqiang Cai, Cuiyu He, Shun Zhang
2021	J	`jnl`	Hybrid A Posteriori Error Estimators for Conforming Finite Element Approximations to Stationary Convection-Diffusion-Reaction equations. CoRR Difeng Cai, Zhiqiang Cai
2021	J	`jnl`	Least-Squares ReLU Neural Network (LSNN) Method For Linear Advection-Reaction Equation. CoRR Zhiqiang Cai, Jingshuang Chen, Min Liu
2021	J	`jnl`	Least-Squares ReLU Neural Network (LSNN) Method For Scalar Nonlinear Hyperbolic Conservation Law. CoRR Zhiqiang Cai, Jingshuang Chen, Min Liu
2021	J	`jnl`	Least-squares ReLU neural network (LSNN) method for linear advection-reaction equation. J. Comput. Phys. Zhiqiang Cai, Jingshuang Chen, Min Liu
2021	J	`jnl`	Self-adaptive deep neural network: Numerical approximation to functions and PDEs. CoRR Zhiqiang Cai, Jingshuang Chen, Min Liu
2020	J	`jnl`	A Dual Finite Element Method for a Singularly Perturbed Reaction-Diffusion Problem. SIAM J. Numer. Anal. Zhiqiang Cai, JaEun Ku
2020	J	`jnl`	Deep least-squares methods: An unsupervised learning-based numerical method for solving elliptic PDEs. J. Comput. Phys. Zhiqiang Cai, Jingshuang Chen, Min Liu, Xinyu Liu
2020	J	`jnl`	Generalized Prager-Synge Inequality and Equilibrated Error Estimators for Discontinuous Elements. CoRR Cuiyu He, Zhiqiang Cai, Shun Zhang
2020	J	`jnl`	Robust Equilibrated Error Estimator for Diffusion Problems: Mixed Finite Elements in Two Dimensions. J. Sci. Comput. Difeng Cai, Zhiqiang Cai, Shun Zhang
2020	J	`jnl`	Robust equilibrated a posteriori error estimator for higher order finite element approximations to diffusion problems. Numerische Mathematik Difeng Cai, Zhiqiang Cai, Shun Zhang
2019	J	`jnl`	Deep least-squares methods: an unsupervised learning-based numerical method for solving elliptic PDEs. CoRR Zhiqiang Cai, Jingshuang Chen, Min Liu, Xinyu Liu
2019	J	`jnl`	Finite Element Method for Two-Sided Fractional Differential Equations with Variable Coefficients: Galerkin Approach. J. Sci. Comput. Zhaopeng Hao, Moongyu Park, Guang Lin, Zhiqiang Cai
2019	J	`jnl`	Least-Squares Methods for Elasticity and Stokes Equations with Weakly Imposed Symmetry. Comput. Methods Appl. Math. Fleurianne Bertrand, Zhiqiang Cai, Eun Young Park
2018	J	`jnl`	Error estimate of a finite element method using stress intensity factor. Comput. Math. Appl. Zhiqiang Cai, Seokchan Kim, Hyung-Chun Lee
2017	J	`jnl`	Discontinuous Finite Element Methods for Interface Problems: Robust A Priori and A Posteriori Error Estimates. SIAM J. Numer. Anal. Zhiqiang Cai, Cuiyu He, Shun Zhang
2017	J	`jnl`	Residual-based a posteriori error estimate for interface problems: Nonconforming linear elements. Math. Comput. Zhiqiang Cai, Cuiyu He, Shun Zhang
2015	J	`jnl`	Asymptotically exact a posteriori error estimators for first-order div least-squares methods in local and global Comput. Math. Appl. Zhiqiang Cai, Varis Carey, JaEun Ku, Eun-Jae Park
2015	J	`jnl`	Div First-Order System LL* (FOSLL*) for Second-Order Elliptic Partial Differential Equations. SIAM J. Numer. Anal. Zhiqiang Cai, Robert D. Falgout, Shun Zhang
2012	J	`jnl`	Mixed methods for stationary Navier-Stokes equations based on pseudostress-pressure-velocity formulation. Math. Comput. Zhiqiang Cai, Shun Zhang
2012	J	`jnl`	Robust Equilibrated Residual Error Estimator for Diffusion Problems: Conforming Elements. SIAM J. Numer. Anal. Zhiqiang Cai, Shun Zhang
2011	J	`jnl`	Discontinuous Galerkin Finite Element Methods for Interface Problems: A Priori and A Posteriori Error Estimations. SIAM J. Numer. Anal. Zhiqiang Cai, Xiu Ye, Shun Zhang
2011	J	`jnl`	Goal-Oriented Local A Posteriori Error Estimators for H(div) Least-Squares Finite Element Methods. SIAM J. Numer. Anal. Zhiqiang Cai, JaEun Ku
2010	J	`jnl`	Flux Recovery and A Posteriori Error Estimators: Conforming Elements for Scalar Elliptic Equations. SIAM J. Numer. Anal. Zhiqiang Cai, Shun Zhang
2010	J	`jnl`	Mixed Finite Element Methods for Incompressible Flow: Stationary Navier-Stokes Equations. SIAM J. Numer. Anal. Zhiqiang Cai, Chunbo Wang, Shun Zhang
2010	J	`jnl`	Optimal Error Estimate for the Div Least-squares Method with Data f∈L SIAM J. Numer. Anal. Zhiqiang Cai, JaEun Ku
2010	J	`jnl`	Recovery-Based Error Estimators for Interface Problems: Mixed and Nonconforming Finite Elements. SIAM J. Numer. Anal. Zhiqiang Cai, Shun Zhang
2009	J	`jnl`	An error estimate for two-dimensional Stokes driven cavity flow. Math. Comput. Zhiqiang Cai, Yanqiu Wang
2009	J	`jnl`	First-Order System Least Squares for the Signorini Contact Problem in Linear Elasticity. SIAM J. Numer. Anal. Frank S. Attia, Zhiqiang Cai, Gerhard Starke
2009	J	`jnl`	Recovery-Based Error Estimator for Interface Problems: Conforming Linear Elements. SIAM J. Numer. Anal. Zhiqiang Cai, Shun Zhang
2008	J	`jnl`	A Weighted H(div) Least-Squares Method for Second-Order Elliptic Problems. SIAM J. Numer. Anal. Zhiqiang Cai, Chad R. Westphal
2007	J	`jnl`	A Multigrid Method for the Pseudostress Formulation of Stokes Problems. SIAM J. Sci. Comput. Zhiqiang Cai, Yanqiu Wang
2006	J	`jnl`	The L SIAM J. Numer. Anal. Zhiqiang Cai, JaEun Ku
2004	J	`jnl`	Least-Squares Methods for Incompressible Newtonian Fluid Flow: Linear Stationary Problems. SIAM J. Numer. Anal. Zhiqiang Cai, Barry Lee, Ping Wang
2004	J	`jnl`	Least-Squares Methods for Linear Elasticity. SIAM J. Numer. Anal. Zhiqiang Cai, Gerhard Starke
2003	J	`jnl`	Development and Analysis of Higher Order Finite Volume Methods over Rectangles for Elliptic Equations. Adv. Comput. Math. Zhiqiang Cai, Jim Douglas Jr., Moongyu Park
2003	J	`jnl`	Domain Decomposition for a Mixed Finite Element Method in Three Dimensions. SIAM J. Numer. Anal. Zhiqiang Cai, Rossen R. Parashkevov, Thomas F. Russell, J. D. Wilson, Xiu Ye
2003	J	`jnl`	First-Order System Least Squares for the Stress-Displacement Formulation: Linear Elasticity. SIAM J. Numer. Anal. Zhiqiang Cai, Gerhard Starke
2002	J	`jnl`	A finite element method using singular functions for the Poisson equation: crack singularities. Numer. Linear Algebra Appl. Zhiqiang Cai, Seokchan Kim, Gyungsoo Woo
2002	J	`jnl`	The Discrete First-Order System Least Squares: The Second-Order Elliptic Boundary Value Problem. SIAM J. Numer. Anal. Zhiqiang Cai, Byeong Chun Shin
2001	J	`jnl`	A Finite Element Method Using Singular Functions for the Poisson Equation: Corner Singularities. SIAM J. Numer. Anal. Zhiqiang Cai, Seokchan Kim
2001	J	`jnl`	First-Order System SIAM J. Numer. Anal. Zhiqiang Cai, Thomas A. Manteuffel, Stephen F. McCormick, John W. Ruge
2001	J	`jnl`	Solution Methods for the Poisson Equation with Corner Singularities: Numerical Results. SIAM J. Sci. Comput. Zhiqiang Cai, Seokchan Kim, Byeong Chun Shin
2000	J	`jnl`	First-Order System Least Squares For Linear Elasticity: Numerical Results. SIAM J. Sci. Comput. Zhiqiang Cai, Chang-Ock Lee, Thomas A. Manteuffel, Stephen F. McCormick
2000	J	`jnl`	First-Order System Least Squares for the Stokes and Linear Elasticity Equations: Further Results. SIAM J. Sci. Comput. Zhiqiang Cai, Chang-Ock Lee, Thomas A. Manteuffel, Stephen F. McCormick
2000	J	`jnl`	Least Squares for the Perturbed Stokes Equations and the Reissner-Mindlin Plate. SIAM J. Numer. Anal. Zhiqiang Cai
1999	J	`jnl`	Convergence of a multiscale finite element method for elliptic problems with rapidly oscillating coefficients. Math. Comput. Thomas Y. Hou, Xiao-Hui Wu, Zhiqiang Cai
1999	J	`jnl`	Least-squares finite element approximations for the Reissner-Mindlin plate. Numer. Linear Algebra Appl. Zhiqiang Cai, Xiu Ye, Huilong Zhang
1996	J	`jnl`	Convergence Estimates of Multilevel Additive and Multiplicative Algorithms for Non-symmetric and Indefinite Problems. Numer. Linear Algebra Appl. Zhiqiang Cai, Chen-Yao G. Lai
1993	J	`jnl`	Multilevel Iteration for Mixed Finite Element Systems with Penalty. SIAM J. Sci. Comput. Zhiqiang Cai, Charles I. Goldstein, Joseph E. Pasciak
1989	J	`jnl`	Computational Complexity of the Schwarz Alternating Procedure. Int. J. High Speed Comput. Zhiqiang Cai, Steve F. McCormick