Zhiqiang Cai

According to our database, Zhiqiang Cai authored at least 62 papers between 1989 and 2024.

Collaborative distances:

• Dijkstra number of four.
• Erdős number of three.

2024

Least-Squares Neural Network (LSNN) Method for Linear Advection-Reaction Equation: Discontinuity Interface.

Zhiqiang Cai, Junpyo Choi, Min Liu

SIAM J. Sci. Comput., 2024

ReLU neural network approximation to piecewise constant functions.

Zhiqiang Cai, Junpyo Choi, Min Liu

CoRR, 2024

Fast Iterative Solver For Neural Network Method: II. 1D Diffusion-Reaction Problems And Data Fitting.

Zhiqiang Cai, Anastassia Doktorova, Robert D. Falgout, César Herrera

CoRR, 2024

Fast Iterative Solver For Neural Network Method: I. 1D Diffusion Problems.

Zhiqiang Cai, Anastassia Doktorova, Robert D. Falgout, César Herrera

CoRR, 2024

2023

Least-squares neural network (LSNN) method for scalar nonlinear hyperbolic conservation laws: Discrete divergence operator.

Zhiqiang Cai, Jingshuang Chen, Min Liu

J. Comput. Appl. Math., December, 2023

Least-Squares Neural Network (LSNN) Method For Linear Advection-Reaction Equation: Non-constant Jumps.

Zhiqiang Cai, Junpyo Choi, Min Liu

CoRR, 2023

Deep Ritz Method with Adaptive Quadrature for Linear Elasticity.

Min Liu, Zhiqiang Cai, Karthik Ramani

CoRR, 2023

Adaptive Least-Squares Methods for Convection-Dominated Diffusion-Reaction Problems.

Zhiqiang Cai, Binghe Chen, Jing Yang

CoRR, 2023

Least-Squares Neural Network (LSNN) Method for Linear Advection-Reaction Equation: General Discontinuous Interface.

Zhiqiang Cai, Junpyo Choi, Min Liu

CoRR, 2023

2022

Self-adaptive deep neural network: Numerical approximation to functions and PDEs.

Zhiqiang Cai, Jingshuang Chen, Min Liu

J. Comput. Phys., 2022

Adaptive two-layer ReLU neural network: I. Best least-squares approximation.

Min Liu, Zhiqiang Cai, Jingshuang Chen

Comput. Math. Appl., 2022

Adaptive two-layer ReLU neural network: II. Ritz approximation to elliptic PDEs.

Min Liu, Zhiqiang Cai

Comput. Math. Appl., 2022

2021

Adaptive Finite Element Method for Dirichlet Boundary Control of Elliptic Partial Differential Equations.

Shaohong Du, Zhiqiang Cai

J. Sci. Comput., 2021

Least-squares ReLU neural network (LSNN) method for linear advection-reaction equation.

Zhiqiang Cai, Jingshuang Chen, Min Liu

J. Comput. Phys., 2021

Generalized Prager-Synge identity and robust equilibrated error estimators for discontinuous elements.

Zhiqiang Cai, Cuiyu He, Shun Zhang

J. Comput. Appl. Math., 2021

Finite Volume Least-Squares Neural Network (FV-LSNN) Method for Scalar Nonlinear Hyperbolic Conservation Laws.

Zhiqiang Cai, Jingshuang Chen, Min Liu

CoRR, 2021

Hybrid A Posteriori Error Estimators for Conforming Finite Element Approximations to Stationary Convection-Diffusion-Reaction equations.

Difeng Cai, Zhiqiang Cai

CoRR, 2021

Least-Squares ReLU Neural Network (LSNN) Method For Scalar Nonlinear Hyperbolic Conservation Law.

Zhiqiang Cai, Jingshuang Chen, Min Liu

CoRR, 2021

2020

A Dual Finite Element Method for a Singularly Perturbed Reaction-Diffusion Problem.

Zhiqiang Cai, JaEun Ku

SIAM J. Numer. Anal., 2020

Robust equilibrated a posteriori error estimator for higher order finite element approximations to diffusion problems.

Difeng Cai, Zhiqiang Cai, Shun Zhang

Numerische Mathematik, 2020

Robust Equilibrated Error Estimator for Diffusion Problems: Mixed Finite Elements in Two Dimensions.

Difeng Cai, Zhiqiang Cai, Shun Zhang

J. Sci. Comput., 2020

Deep least-squares methods: An unsupervised learning-based numerical method for solving elliptic PDEs.

Zhiqiang Cai, Jingshuang Chen, Min Liu, Xinyu Liu

J. Comput. Phys., 2020

Generalized Prager-Synge Inequality and Equilibrated Error Estimators for Discontinuous Elements.

Cuiyu He, Zhiqiang Cai, Shun Zhang

CoRR, 2020

2019

Finite Element Method for Two-Sided Fractional Differential Equations with Variable Coefficients: Galerkin Approach.

Zhaopeng Hao, Moongyu Park, Guang Lin, Zhiqiang Cai

J. Sci. Comput., 2019

Least-Squares Methods for Elasticity and Stokes Equations with Weakly Imposed Symmetry.

Fleurianne Bertrand, Zhiqiang Cai, Eun Young Park

Comput. Methods Appl. Math., 2019

2018

Error estimate of a finite element method using stress intensity factor.

Zhiqiang Cai, Seokchan Kim, Hyung-Chun Lee

Comput. Math. Appl., 2018

2017

Discontinuous Finite Element Methods for Interface Problems: Robust A Priori and A Posteriori Error Estimates.

Zhiqiang Cai, Cuiyu He, Shun Zhang

SIAM J. Numer. Anal., 2017

Residual-based a posteriori error estimate for interface problems: Nonconforming linear elements.

Zhiqiang Cai, Cuiyu He, Shun Zhang

Math. Comput., 2017

2015

Div First-Order System LL* (FOSLL*) for Second-Order Elliptic Partial Differential Equations.

Zhiqiang Cai, Robert D. Falgout, Shun Zhang

SIAM J. Numer. Anal., 2015

Asymptotically exact a posteriori error estimators for first-order div least-squares methods in local and global _L₂ norm.

Zhiqiang Cai, Varis Carey, JaEun Ku, Eun-Jae Park

Comput. Math. Appl., 2015

2012

Robust Equilibrated Residual Error Estimator for Diffusion Problems: Conforming Elements.

Zhiqiang Cai, Shun Zhang

SIAM J. Numer. Anal., 2012

Mixed methods for stationary Navier-Stokes equations based on pseudostress-pressure-velocity formulation.

Zhiqiang Cai, Shun Zhang

Math. Comput., 2012

2011

Discontinuous Galerkin Finite Element Methods for Interface Problems: A Priori and A Posteriori Error Estimations.

Zhiqiang Cai, Xiu Ye, Shun Zhang

SIAM J. Numer. Anal., 2011

Goal-Oriented Local A Posteriori Error Estimators for H(div) Least-Squares Finite Element Methods.

Zhiqiang Cai, JaEun Ku

SIAM J. Numer. Anal., 2011

2010

Flux Recovery and A Posteriori Error Estimators: Conforming Elements for Scalar Elliptic Equations.

Zhiqiang Cai, Shun Zhang

SIAM J. Numer. Anal., 2010

Recovery-Based Error Estimators for Interface Problems: Mixed and Nonconforming Finite Elements.

Zhiqiang Cai, Shun Zhang

SIAM J. Numer. Anal., 2010

Mixed Finite Element Methods for Incompressible Flow: Stationary Navier-Stokes Equations.

Zhiqiang Cai, Chunbo Wang, Shun Zhang

SIAM J. Numer. Anal., 2010

Optimal Error Estimate for the Div Least-squares Method with Data f∈L² and Application to Nonlinear Problems.

Zhiqiang Cai, JaEun Ku

SIAM J. Numer. Anal., 2010

2009

Recovery-Based Error Estimator for Interface Problems: Conforming Linear Elements.

Zhiqiang Cai, Shun Zhang

SIAM J. Numer. Anal., 2009

First-Order System Least Squares for the Signorini Contact Problem in Linear Elasticity.

Frank S. Attia, Zhiqiang Cai, Gerhard Starke

SIAM J. Numer. Anal., 2009

An error estimate for two-dimensional Stokes driven cavity flow.

Zhiqiang Cai, Yanqiu Wang

Math. Comput., 2009

2008

A Weighted H(div) Least-Squares Method for Second-Order Elliptic Problems.

Zhiqiang Cai, Chad R. Westphal

SIAM J. Numer. Anal., 2008

2007

A Multigrid Method for the Pseudostress Formulation of Stokes Problems.

Zhiqiang Cai, Yanqiu Wang

SIAM J. Sci. Comput., 2007

2006

The L² Norm Error Estimates for the Div Least-Squares Method.

Zhiqiang Cai, JaEun Ku

SIAM J. Numer. Anal., 2006

2004

Least-Squares Methods for Linear Elasticity.

Zhiqiang Cai, Gerhard Starke

SIAM J. Numer. Anal., 2004

Least-Squares Methods for Incompressible Newtonian Fluid Flow: Linear Stationary Problems.

Zhiqiang Cai, Barry Lee, Ping Wang

SIAM J. Numer. Anal., 2004

2003

First-Order System Least Squares for the Stress-Displacement Formulation: Linear Elasticity.

Zhiqiang Cai, Gerhard Starke

SIAM J. Numer. Anal., 2003

Domain Decomposition for a Mixed Finite Element Method in Three Dimensions.

Zhiqiang Cai, Rossen R. Parashkevov, Thomas F. Russell, J. D. Wilson, Xiu Ye

SIAM J. Numer. Anal., 2003

Development and Analysis of Higher Order Finite Volume Methods over Rectangles for Elliptic Equations.

Zhiqiang Cai, Jim Douglas Jr., Moongyu Park

Adv. Comput. Math., 2003

2002

The Discrete First-Order System Least Squares: The Second-Order Elliptic Boundary Value Problem.

Zhiqiang Cai, Byeong Chun Shin

SIAM J. Numer. Anal., 2002

A finite element method using singular functions for the Poisson equation: crack singularities.

Zhiqiang Cai, Seokchan Kim, Gyungsoo Woo

Numer. Linear Algebra Appl., 2002

2001

Solution Methods for the Poisson Equation with Corner Singularities: Numerical Results.

Zhiqiang Cai, Seokchan Kim, Byeong Chun Shin

SIAM J. Sci. Comput., 2001

First-Order System <i>\CL\CL^*</i> (FOSLL*): Scalar Elliptic Partial Differential Equations.

Zhiqiang Cai, Thomas A. Manteuffel, Stephen F. McCormick, John W. Ruge

SIAM J. Numer. Anal., 2001

A Finite Element Method Using Singular Functions for the Poisson Equation: Corner Singularities.

Zhiqiang Cai, Seokchan Kim

SIAM J. Numer. Anal., 2001

2000

First-Order System Least Squares for the Stokes and Linear Elasticity Equations: Further Results.

Zhiqiang Cai, Chang-Ock Lee, Thomas A. Manteuffel, Stephen F. McCormick

SIAM J. Sci. Comput., 2000

First-Order System Least Squares For Linear Elasticity: Numerical Results.

Zhiqiang Cai, Chang-Ock Lee, Thomas A. Manteuffel, Stephen F. McCormick

SIAM J. Sci. Comput., 2000

Least Squares for the Perturbed Stokes Equations and the Reissner-Mindlin Plate.

Zhiqiang Cai

SIAM J. Numer. Anal., 2000

1999

Least-squares finite element approximations for the Reissner-Mindlin plate.

Zhiqiang Cai, Xiu Ye, Huilong Zhang

Numer. Linear Algebra Appl., 1999

Convergence of a multiscale finite element method for elliptic problems with rapidly oscillating coefficients.

Thomas Y. Hou, Xiao-hui Wu, Zhiqiang Cai

Math. Comput., 1999

1996

Convergence Estimates of Multilevel Additive and Multiplicative Algorithms for Non-symmetric and Indefinite Problems.

Zhiqiang Cai, Chen-Yao G. Lai

Numer. Linear Algebra Appl., 1996

1993

Multilevel Iteration for Mixed Finite Element Systems with Penalty.

Zhiqiang Cai, Charles I. Goldstein, Joseph E. Pasciak

SIAM J. Sci. Comput., 1993

1989

Computational Complexity of the Schwarz Alternating Procedure.

Zhiqiang Cai, Steve F. McCormick

Int. J. High Speed Comput., 1989