Computational Complexity of the Schwarz Alternating Procedure. - Zhiqiang Cai 001; Steve F. McCormick (Int. J. High Speed Comput., 1989)

Multilevel Iteration for Mixed Finite Element Systems with Penalty. - Zhiqiang Cai 001; Charles I. Goldstein; Joseph E. Pasciak (SIAM J. Sci. Comput., 1993)

Convergence Estimates of Multilevel Additive and Multiplicative Algorithms for Non-symmetric and Indefinite Problems. - Zhiqiang Cai 001; Chen-Yao G. Lai (Numer. Linear Algebra Appl., 1996)

Convergence of a multiscale finite element method for elliptic problems with rapidly oscillating coefficients. - Thomas Y. Hou 001; Xiao-hui Wu; Zhiqiang Cai 001 (Math. Comput., 1999)

Least-squares finite element approximations for the Reissner-Mindlin plate. - Zhiqiang Cai 001; Xiu Ye; Huilong Zhang (Numer. Linear Algebra Appl., 1999)

Least Squares for the Perturbed Stokes Equations and the Reissner-Mindlin Plate. - Zhiqiang Cai 001 (SIAM J. Numer. Anal., 2000)

First-Order System Least Squares For Linear Elasticity: Numerical Results. - Zhiqiang Cai 001; Chang-Ock Lee; Thomas A. Manteuffel; Stephen F. McCormick (SIAM J. Sci. Comput., 2000)

First-Order System Least Squares for the Stokes and Linear Elasticity Equations: Further Results. - Zhiqiang Cai 001; Chang-Ock Lee; Thomas A. Manteuffel; Stephen F. McCormick (SIAM J. Sci. Comput., 2000)

A Finite Element Method Using Singular Functions for the Poisson Equation: Corner Singularities. - Zhiqiang Cai 001; Seokchan Kim (SIAM J. Numer. Anal., 2001)

First-Order System CL CL* (FOSLL*): Scalar Elliptic Partial Differential Equations. - Zhiqiang Cai 001; Thomas A. Manteuffel; Stephen F. McCormick; John W. Ruge (SIAM J. Numer. Anal., 2001)

Solution Methods for the Poisson Equation with Corner Singularities: Numerical Results. - Zhiqiang Cai 001; Seokchan Kim; Byeong Chun Shin (SIAM J. Sci. Comput., 2001)

A finite element method using singular functions for the Poisson equation: crack singularities. - Zhiqiang Cai 001; Seokchan Kim; Gyungsoo Woo (Numer. Linear Algebra Appl., 2002)

The Discrete First-Order System Least Squares: The Second-Order Elliptic Boundary Value Problem. - Zhiqiang Cai 001; Byeong Chun Shin (SIAM J. Numer. Anal., 2002)

Development and Analysis of Higher Order Finite Volume Methods over Rectangles for Elliptic Equations. - Zhiqiang Cai 001; Jim Douglas Jr.; Moongyu Park (Adv. Comput. Math., 2003)

Domain Decomposition for a Mixed Finite Element Method in Three Dimensions. - Zhiqiang Cai 001; Rossen R. Parashkevov; Thomas F. Russell; J. D. Wilson; Xiu Ye (SIAM J. Numer. Anal., 2003)

First-Order System Least Squares for the Stress-Displacement Formulation: Linear Elasticity. - Zhiqiang Cai 001; Gerhard Starke (SIAM J. Numer. Anal., 2003)

Least-Squares Methods for Incompressible Newtonian Fluid Flow: Linear Stationary Problems. - Zhiqiang Cai 001; Barry Lee; Ping Wang (SIAM J. Numer. Anal., 2004)

Least-Squares Methods for Linear Elasticity. - Zhiqiang Cai 001; Gerhard Starke (SIAM J. Numer. Anal., 2004)

The L2 Norm Error Estimates for the Div Least-Squares Method. - Zhiqiang Cai 001; JaEun Ku (SIAM J. Numer. Anal., 2006)

A Multigrid Method for the Pseudostress Formulation of Stokes Problems. - Zhiqiang Cai 001; Yanqiu Wang (SIAM J. Sci. Comput., 2007)

A Weighted H(div) Least-Squares Method for Second-Order Elliptic Problems. - Zhiqiang Cai 001; Chad R. Westphal (SIAM J. Numer. Anal., 2008)

An error estimate for two-dimensional Stokes driven cavity flow. - Zhiqiang Cai 001; Yanqiu Wang (Math. Comput., 2009)

First-Order System Least Squares for the Signorini Contact Problem in Linear Elasticity. - Frank S. Attia; Zhiqiang Cai 001; Gerhard Starke (SIAM J. Numer. Anal., 2009)

Recovery-Based Error Estimator for Interface Problems: Conforming Linear Elements. - Zhiqiang Cai 001; Shun Zhang 001 (SIAM J. Numer. Anal., 2009)

Optimal Error Estimate for the Div Least-squares Method with Data f∈L2 and Application to Nonlinear Problems. - Zhiqiang Cai 001; JaEun Ku (SIAM J. Numer. Anal., 2010)

Mixed Finite Element Methods for Incompressible Flow: Stationary Navier-Stokes Equations. - Zhiqiang Cai 001; Chunbo Wang; Shun Zhang 001 (SIAM J. Numer. Anal., 2010)

Recovery-Based Error Estimators for Interface Problems: Mixed and Nonconforming Finite Elements. - Zhiqiang Cai 001; Shun Zhang 001 (SIAM J. Numer. Anal., 2010)

Flux Recovery and A Posteriori Error Estimators: Conforming Elements for Scalar Elliptic Equations. - Zhiqiang Cai 001; Shun Zhang 001 (SIAM J. Numer. Anal., 2010)

Goal-Oriented Local A Posteriori Error Estimators for H(div) Least-Squares Finite Element Methods. - Zhiqiang Cai 001; JaEun Ku (SIAM J. Numer. Anal., 2011)

Discontinuous Galerkin Finite Element Methods for Interface Problems: A Priori and A Posteriori Error Estimations. - Zhiqiang Cai 001; Xiu Ye; Shun Zhang 001 (SIAM J. Numer. Anal., 2011)

Mixed methods for stationary Navier-Stokes equations based on pseudostress-pressure-velocity formulation. - Zhiqiang Cai 001; Shun Zhang 001 (Math. Comput., 2012)

Robust Equilibrated Residual Error Estimator for Diffusion Problems: Conforming Elements. - Zhiqiang Cai 001; Shun Zhang 001 (SIAM J. Numer. Anal., 2012)

Asymptotically exact a posteriori error estimators for first-order div least-squares methods in local and global L2 norm. - Zhiqiang Cai 001; Varis Carey; JaEun Ku; Eun-Jae Park (Comput. Math. Appl., 2015)

Div First-Order System LL* (FOSLL*) for Second-Order Elliptic Partial Differential Equations. - Zhiqiang Cai 001; Robert D. Falgout; Shun Zhang 001 (SIAM J. Numer. Anal., 2015)

Residual-based a posteriori error estimate for interface problems: Nonconforming linear elements. - Zhiqiang Cai 001; Cuiyu He; Shun Zhang 001 (Math. Comput., 2017)

Discontinuous Finite Element Methods for Interface Problems: Robust A Priori and A Posteriori Error Estimates. - Zhiqiang Cai 001; Cuiyu He; Shun Zhang 001 (SIAM J. Numer. Anal., 2017)

Error estimate of a finite element method using stress intensity factor. - Zhiqiang Cai 001; Seokchan Kim; Hyung-Chun Lee (Comput. Math. Appl., 2018)

Least-Squares Methods for Elasticity and Stokes Equations with Weakly Imposed Symmetry. - Fleurianne Bertrand; Zhiqiang Cai 001; Eun Young Park (Comput. Methods Appl. Math., 2019)

Finite Element Method for Two-Sided Fractional Differential Equations with Variable Coefficients: Galerkin Approach. - Zhaopeng Hao; Moongyu Park; Guang Lin 001; Zhiqiang Cai 001 (J. Sci. Comput., 2019)

Generalized Prager-Synge Inequality and Equilibrated Error Estimators for Discontinuous Elements. - Cuiyu He; Zhiqiang Cai 001; Shun Zhang 001 (CoRR, 2020)

Deep least-squares methods: An unsupervised learning-based numerical method for solving elliptic PDEs. - Zhiqiang Cai 001; Jingshuang Chen; Min Liu 018; Xinyu Liu (J. Comput. Phys., 2020)

Robust Equilibrated Error Estimator for Diffusion Problems: Mixed Finite Elements in Two Dimensions. - Difeng Cai; Zhiqiang Cai 001; Shun Zhang 001 (J. Sci. Comput., 2020)

Robust equilibrated a posteriori error estimator for higher order finite element approximations to diffusion problems. - Difeng Cai; Zhiqiang Cai 001; Shun Zhang 001 (Numerische Mathematik, 2020)

A Dual Finite Element Method for a Singularly Perturbed Reaction-Diffusion Problem. - Zhiqiang Cai 001; JaEun Ku (SIAM J. Numer. Anal., 2020)

Least-Squares ReLU Neural Network (LSNN) Method For Scalar Nonlinear Hyperbolic Conservation Law. - Zhiqiang Cai 001; Jingshuang Chen; Min Liu 018 (CoRR, 2021)

Finite Volume Least-Squares Neural Network (FV-LSNN) Method for Scalar Nonlinear Hyperbolic Conservation Laws. - Zhiqiang Cai 001; Jingshuang Chen; Min Liu 018 (CoRR, 2021)

Generalized Prager-Synge identity and robust equilibrated error estimators for discontinuous elements. - Zhiqiang Cai 001; Cuiyu He; Shun Zhang 001 (J. Comput. Appl. Math., 2021)

Least-squares ReLU neural network (LSNN) method for linear advection-reaction equation. - Zhiqiang Cai 001; Jingshuang Chen; Min Liu 018 (J. Comput. Phys., 2021)

Adaptive Finite Element Method for Dirichlet Boundary Control of Elliptic Partial Differential Equations. - Shaohong Du; Zhiqiang Cai 001 (J. Sci. Comput., 2021)

Adaptive two-layer ReLU neural network: II. Ritz approximation to elliptic PDEs. - Min Liu 018; Zhiqiang Cai 001 (Comput. Math. Appl., 2022)

Adaptive two-layer ReLU neural network: I. Best least-squares approximation. - Min Liu 018; Zhiqiang Cai 001; Jingshuang Chen (Comput. Math. Appl., 2022)

Self-adaptive deep neural network: Numerical approximation to functions and PDEs. - Zhiqiang Cai 001; Jingshuang Chen; Min Liu 018 (J. Comput. Phys., 2022)

Least-Squares Neural Network (LSNN) Method for Linear Advection-Reaction Equation: General Discontinuous Interface. - Zhiqiang Cai 001; Junpyo Choi; Min Liu 018 (CoRR, 2023)

Adaptive Least-Squares Methods for Convection-Dominated Diffusion-Reaction Problems. - Zhiqiang Cai 001; Binghe Chen; Jing Yang (CoRR, 2023)

Deep Ritz Method with Adaptive Quadrature for Linear Elasticity. - Min Liu 018; Zhiqiang Cai 001; Karthik Ramani (CoRR, 2023)

Least-Squares Neural Network (LSNN) Method For Linear Advection-Reaction Equation: Non-constant Jumps. - Zhiqiang Cai 001; Junpyo Choi; Min Liu 018 (CoRR, 2023)

Optimal error estimate of discontinuous Galerkin methods for advection-diffusion-reaction problems with low regularity. - Zhiqiang Cai 001; Jing Yang (Comput. Math. Appl., 2023)

Least-squares neural network (LSNN) method for scalar nonlinear hyperbolic conservation laws: Discrete divergence operator. - Zhiqiang Cai 001; Jingshuang Chen; Min Liu 018 (J. Comput. Appl. Math., 2023)

Fast Iterative Solver For Neural Network Method: I. 1D Diffusion Problems. - Zhiqiang Cai 001; Anastassia Doktorova; Robert D. Falgout; César Herrera (CoRR, 2024)

Fast Iterative Solver For Neural Network Method: II. 1D Diffusion-Reaction Problems And Data Fitting. - Zhiqiang Cai 001; Anastassia Doktorova; Robert D. Falgout; César Herrera (CoRR, 2024)

ReLU neural network approximation to piecewise constant functions. - Zhiqiang Cai 001; Junpyo Choi; Min Liu 018 (CoRR, 2024)

Fractional-order dependent Radial basis functions meshless methods for the integral fractional Laplacian. - Zhaopeng Hao; Zhiqiang Cai 001; Zhongqiang Zhang (CoRR, 2024)

Least-Squares Neural Network (LSNN) Method for Linear Advection-Reaction Equation: Discontinuity Interface. - Zhiqiang Cai 001; Junpyo Choi; Min Liu 018 (SIAM J. Sci. Comput., 2024)

Dual Neural Network (DuNN) method for elliptic partial differential equations and systems. - Min Liu 018; Zhiqiang Cai 001; Karthik Ramani (J. Comput. Appl. Math., 2025)

Hybrid a posteriori error estimators for conforming finite element approximations to stationary convection-diffusion-reaction equations. - Difeng Cai; Zhiqiang Cai 001 (Numerische Mathematik, 2025)