Stop the war!Остановите войну!
for scientists:
default search action
Google
Google Scholar
Semantic Scholar
Internet Archive Scholar
CiteSeerX
ORCIDZhiqiang Cai 0001
Person information
- affiliation: Purdue University, Department of Mathematics, West Lafayette, IN, USA
Other persons with the same name
- Zhiqiang Cai — disambiguation page
- Zhiqiang Cai 0002
![[0000-0002-2107-3378]](https://dblp.uni-trier.de/img/orcid-mark.12x12.png "0000-0002-2107-3378")
— University of Wisconsin-Madison, WI, USA (and 1 more) - Zhiqiang Cai 0003 — Northwestern Polytechnical University, School of Mechanical Engineering, Xi'an, China
- Zhiqiang Cai 0004 — City University of Hong Kong, Hong Kong
- Zhiqiang Cai 0005 — Tongji University, School of Electronics and Information, China
- Zhiqiang Cai 0006 — Harbin University of Science and Technology, School of Electrical and Electronic Engineering, China
Refine list
refinements active!
zoomed in on ?? of ?? records
view refined list in
export refined list as
Journal Articles
- 2023
[j50]Zhiqiang Cai, Jingshuang Chen, Min Liu:
Least-squares neural network (LSNN) method for scalar nonlinear hyperbolic conservation laws: Discrete divergence operator. J. Comput. Appl. Math. 433: 115298 (2023)- 2022
- [j49]Min Liu, Zhiqiang Cai, Jingshuang Chen:
Adaptive two-layer ReLU neural network: I. Best least-squares approximation. Comput. Math. Appl. 113: 34-44 (2022) - [j48]Min Liu, Zhiqiang Cai:
Adaptive two-layer ReLU neural network: II. Ritz approximation to elliptic PDEs. Comput. Math. Appl. 113: 103-116 (2022) - [j47]Zhiqiang Cai, Jingshuang Chen, Min Liu:
Self-adaptive deep neural network: Numerical approximation to functions and PDEs. J. Comput. Phys. 455: 111021 (2022) - 2021
- [j46]Zhiqiang Cai, Cuiyu He, Shun Zhang:
Generalized Prager-Synge identity and robust equilibrated error estimators for discontinuous elements. J. Comput. Appl. Math. 398: 113673 (2021) - [j45]Zhiqiang Cai, Jingshuang Chen, Min Liu:
Least-squares ReLU neural network (LSNN) method for linear advection-reaction equation. J. Comput. Phys. 443: 110514 (2021) - [j44]Shaohong Du, Zhiqiang Cai:
Adaptive Finite Element Method for Dirichlet Boundary Control of Elliptic Partial Differential Equations. J. Sci. Comput. 89(2): 36 (2021) - 2020
- [j43]Zhiqiang Cai, Jingshuang Chen, Min Liu, Xinyu Liu:
Deep least-squares methods: An unsupervised learning-based numerical method for solving elliptic PDEs. J. Comput. Phys. 420: 109707 (2020) - [j42]Difeng Cai, Zhiqiang Cai, Shun Zhang:
Robust Equilibrated Error Estimator for Diffusion Problems: Mixed Finite Elements in Two Dimensions. J. Sci. Comput. 83(1): 22 (2020) - [j41]Difeng Cai, Zhiqiang Cai, Shun Zhang:
Robust equilibrated a posteriori error estimator for higher order finite element approximations to diffusion problems. Numerische Mathematik 144(1): 1-21 (2020) - [j40]Zhiqiang Cai, JaEun Ku:
A Dual Finite Element Method for a Singularly Perturbed Reaction-Diffusion Problem. SIAM J. Numer. Anal. 58(3): 1654-1673 (2020) - 2019
- [j39]Fleurianne Bertrand, Zhiqiang Cai, Eun Young Park:
Least-Squares Methods for Elasticity and Stokes Equations with Weakly Imposed Symmetry. Comput. Methods Appl. Math. 19(3): 415-430 (2019) - [j38]Zhaopeng Hao, Moongyu Park, Guang Lin, Zhiqiang Cai:
Finite Element Method for Two-Sided Fractional Differential Equations with Variable Coefficients: Galerkin Approach. J. Sci. Comput. 79(2): 700-717 (2019) - 2018
- [j37]Zhiqiang Cai, Seokchan Kim, Hyung-Chun Lee:
Error estimate of a finite element method using stress intensity factor. Comput. Math. Appl. 76(10): 2402-2408 (2018) - 2017
- [j36]Zhiqiang Cai, Cuiyu He, Shun Zhang:
Residual-based a posteriori error estimate for interface problems: Nonconforming linear elements. Math. Comput. 86(304): 617-636 (2017) - [j35]Zhiqiang Cai, Cuiyu He, Shun Zhang:
Discontinuous Finite Element Methods for Interface Problems: Robust A Priori and A Posteriori Error Estimates. SIAM J. Numer. Anal. 55(1): 400-418 (2017) - 2015
- [j34]Zhiqiang Cai, Varis Carey, JaEun Ku, Eun-Jae Park:
Asymptotically exact a posteriori error estimators for first-order div least-squares methods in local and global L2 norm. Comput. Math. Appl. 70(4): 648-659 (2015) - [j33]Zhiqiang Cai, Robert D. Falgout, Shun Zhang:
Div First-Order System LL* (FOSLL*) for Second-Order Elliptic Partial Differential Equations. SIAM J. Numer. Anal. 53(1): 405-420 (2015) - 2012
- [j32]Zhiqiang Cai, Shun Zhang:
Mixed methods for stationary Navier-Stokes equations based on pseudostress-pressure-velocity formulation. Math. Comput. 81(280): 1903-1927 (2012) - [j31]Zhiqiang Cai, Shun Zhang:
Robust Equilibrated Residual Error Estimator for Diffusion Problems: Conforming Elements. SIAM J. Numer. Anal. 50(1): 151-170 (2012) - 2011
- [j30]Zhiqiang Cai, Xiu Ye, Shun Zhang:
Discontinuous Galerkin Finite Element Methods for Interface Problems: A Priori and A Posteriori Error Estimations. SIAM J. Numer. Anal. 49(5): 1761-1787 (2011) - [j29]Zhiqiang Cai, JaEun Ku:
Goal-Oriented Local A Posteriori Error Estimators for H(div) Least-Squares Finite Element Methods. SIAM J. Numer. Anal. 49(6): 2564-2575 (2011) - 2010
- [j28]Zhiqiang Cai, JaEun Ku:
Optimal Error Estimate for the Div Least-squares Method with Data f∈L2 and Application to Nonlinear Problems. SIAM J. Numer. Anal. 47(6): 4098-4111 (2010) - [j27]Zhiqiang Cai, Shun Zhang:
Recovery-Based Error Estimators for Interface Problems: Mixed and Nonconforming Finite Elements. SIAM J. Numer. Anal. 48(1): 30-52 (2010) - [j26]Zhiqiang Cai, Chunbo Wang, Shun Zhang:
Mixed Finite Element Methods for Incompressible Flow: Stationary Navier-Stokes Equations. SIAM J. Numer. Anal. 48(1): 79-94 (2010) - [j25]Zhiqiang Cai, Shun Zhang:
Flux Recovery and A Posteriori Error Estimators: Conforming Elements for Scalar Elliptic Equations. SIAM J. Numer. Anal. 48(2): 578-602 (2010) - 2009
- [j24]Zhiqiang Cai, Yanqiu Wang:
An error estimate for two-dimensional Stokes driven cavity flow. Math. Comput. 78(266): 771-787 (2009) - [j23]Zhiqiang Cai, Shun Zhang:
Recovery-Based Error Estimator for Interface Problems: Conforming Linear Elements. SIAM J. Numer. Anal. 47(3): 2132-2156 (2009) - [j22]Frank S. Attia, Zhiqiang Cai, Gerhard Starke:
First-Order System Least Squares for the Signorini Contact Problem in Linear Elasticity. SIAM J. Numer. Anal. 47(4): 3027-3043 (2009) - 2008
- [j21]Zhiqiang Cai, Chad R. Westphal:
A Weighted H(div) Least-Squares Method for Second-Order Elliptic Problems. SIAM J. Numer. Anal. 46(3): 1640-1651 (2008) - 2007
- [j20]Zhiqiang Cai, Yanqiu Wang:
A Multigrid Method for the Pseudostress Formulation of Stokes Problems. SIAM J. Sci. Comput. 29(5): 2078-2095 (2007) - 2006
- [j19]Zhiqiang Cai, JaEun Ku:
The L2 Norm Error Estimates for the Div Least-Squares Method. SIAM J. Numer. Anal. 44(4): 1721-1734 (2006) - 2004
- [j18]Zhiqiang Cai, Gerhard Starke:
Least-Squares Methods for Linear Elasticity. SIAM J. Numer. Anal. 42(2): 826-842 (2004) - [j17]Zhiqiang Cai, Barry Lee, Ping Wang:
Least-Squares Methods for Incompressible Newtonian Fluid Flow: Linear Stationary Problems. SIAM J. Numer. Anal. 42(2): 843-859 (2004) - 2003
- [j16]Zhiqiang Cai, Jim Douglas Jr., Moongyu Park:
Development and Analysis of Higher Order Finite Volume Methods over Rectangles for Elliptic Equations. Adv. Comput. Math. 19(1-3): 3-33 (2003) - [j15]Zhiqiang Cai, Rossen R. Parashkevov, Thomas F. Russell, J. D. Wilson, Xiu Ye:
Domain Decomposition for a Mixed Finite Element Method in Three Dimensions. SIAM J. Numer. Anal. 41(1): 181-194 (2003) - [j14]Zhiqiang Cai, Gerhard Starke:
First-Order System Least Squares for the Stress-Displacement Formulation: Linear Elasticity. SIAM J. Numer. Anal. 41(2): 715-730 (2003) - 2002
- [j13]Zhiqiang Cai, Seokchan Kim, Gyungsoo Woo:
A finite element method using singular functions for the Poisson equation: crack singularities. Numer. Linear Algebra Appl. 9(6-7): 445-455 (2002) - [j12]Zhiqiang Cai, Byeong Chun Shin:
The Discrete First-Order System Least Squares: The Second-Order Elliptic Boundary Value Problem. SIAM J. Numer. Anal. 40(1): 307-318 (2002) - 2001
- [j11]Zhiqiang Cai, Seokchan Kim:
A Finite Element Method Using Singular Functions for the Poisson Equation: Corner Singularities. SIAM J. Numer. Anal. 39(1): 286-299 (2001) - [j10]Zhiqiang Cai, Thomas A. Manteuffel, Stephen F. McCormick, John W. Ruge:
First-Order System \CL\CL* (FOSLL*): Scalar Elliptic Partial Differential Equations. SIAM J. Numer. Anal. 39(4): 1418-1445 (2001) - [j9]Zhiqiang Cai, Seokchan Kim, Byeong Chun Shin:
Solution Methods for the Poisson Equation with Corner Singularities: Numerical Results. SIAM J. Sci. Comput. 23(2): 672-682 (2001) - 2000
- [j8]Zhiqiang Cai:
Least Squares for the Perturbed Stokes Equations and the Reissner-Mindlin Plate. SIAM J. Numer. Anal. 38(5): 1561-1581 (2000) - [j7]Zhiqiang Cai, Chang-Ock Lee, Thomas A. Manteuffel, Stephen F. McCormick:
First-Order System Least Squares For Linear Elasticity: Numerical Results. SIAM J. Sci. Comput. 21(5): 1706-1727 (2000) - [j6]Zhiqiang Cai, Chang-Ock Lee, Thomas A. Manteuffel, Stephen F. McCormick:
First-Order System Least Squares for the Stokes and Linear Elasticity Equations: Further Results. SIAM J. Sci. Comput. 21(5): 1728-1739 (2000) - 1999
- [j5]Thomas Y. Hou, Xiao-hui Wu, Zhiqiang Cai:
Convergence of a multiscale finite element method for elliptic problems with rapidly oscillating coefficients. Math. Comput. 68(227): 913-943 (1999) - [j4]Zhiqiang Cai, Xiu Ye, Huilong Zhang:
Least-squares finite element approximations for the Reissner-Mindlin plate. Numer. Linear Algebra Appl. 6(6): 479-496 (1999) - 1996
- [j3]Zhiqiang Cai, Chen-Yao G. Lai:
Convergence Estimates of Multilevel Additive and Multiplicative Algorithms for Non-symmetric and Indefinite Problems. Numer. Linear Algebra Appl. 3(3): 205-220 (1996) - 1993
- [j2]Zhiqiang Cai, Charles I. Goldstein, Joseph E. Pasciak:
Multilevel Iteration for Mixed Finite Element Systems with Penalty. SIAM J. Sci. Comput. 14(5): 1072-1088 (1993) - 1989
- [j1]Zhiqiang Cai, Steve F. McCormick:
Computational Complexity of the Schwarz Alternating Procedure. Int. J. High Speed Comput. 1(1): 1-28 (1989)
Informal and Other Publications
- 2024
- [i14]Zhiqiang Cai, Anastassia Doktorova, Robert D. Falgout, César Herrera:
Fast Iterative Solver For Neural Network Method: I. 1D Diffusion Problems. CoRR abs/2404.17750 (2024) - 2023
- [i13]Zhiqiang Cai, Junpyo Choi, Min Liu:
Least-Squares Neural Network (LSNN) Method for Linear Advection-Reaction Equation: General Discontinuous Interface. CoRR abs/2301.06156 (2023) - [i12]Zhiqiang Cai, Binghe Chen, Jing Yang:
Adaptive Least-Squares Methods for Convection-Dominated Diffusion-Reaction Problems. CoRR abs/2301.11582 (2023) - [i11]Min Liu, Zhiqiang Cai, Karthik Ramani:
Deep Ritz Method with Adaptive Quadrature for Linear Elasticity. CoRR abs/2305.15257 (2023) - [i10]Zhiqiang Cai, Junpyo Choi, Min Liu:
Least-Squares Neural Network (LSNN) Method For Linear Advection-Reaction Equation: Non-constant Jumps. CoRR abs/2306.07445 (2023) - 2021
- [i9]Zhiqiang Cai, Jingshuang Chen, Min Liu:
Least-Squares ReLU Neural Network (LSNN) Method For Scalar Nonlinear Hyperbolic Conservation Law. CoRR abs/2105.11627 (2021) - [i8]Zhiqiang Cai, Jingshuang Chen, Min Liu:
Least-Squares ReLU Neural Network (LSNN) Method For Linear Advection-Reaction Equation. CoRR abs/2105.11632 (2021) - [i7]Difeng Cai, Zhiqiang Cai:
Hybrid A Posteriori Error Estimators for Conforming Finite Element Approximations to Stationary Convection-Diffusion-Reaction equations. CoRR abs/2107.06341 (2021) - [i6]Min Liu, Zhiqiang Cai:
Adaptive Two-Layer ReLU Neural Network: II. Ritz Approximation to Elliptic PDEs. CoRR abs/2107.06459 (2021) - [i5]Min Liu, Zhiqiang Cai, Jingshuang Chen:
Adaptive Two-Layer ReLU Neural Network: I. Best Least-squares Approximation. CoRR abs/2107.08935 (2021) - [i4]Zhiqiang Cai, Jingshuang Chen, Min Liu:
Self-adaptive deep neural network: Numerical approximation to functions and PDEs. CoRR abs/2109.02839 (2021) - [i3]Zhiqiang Cai, Jingshuang Chen, Min Liu:
Finite Volume Least-Squares Neural Network (FV-LSNN) Method for Scalar Nonlinear Hyperbolic Conservation Laws. CoRR abs/2110.10895 (2021) - 2020
- [i2]Cuiyu He, Zhiqiang Cai, Shun Zhang:
Generalized Prager-Synge Inequality and Equilibrated Error Estimators for Discontinuous Elements. CoRR abs/2001.09102 (2020) - 2019
- [i1]Zhiqiang Cai, Jingshuang Chen, Min Liu, Xinyu Liu:
Deep least-squares methods: an unsupervised learning-based numerical method for solving elliptic PDEs. CoRR abs/1911.02109 (2019)
Coauthor Index
manage site settings
To protect your privacy, all features that rely on external API calls from your browser are turned off by default. You need to opt-in for them to become active. All settings here will be stored as cookies with your web browser. For more information see our F.A.Q.
Unpaywalled article links
Add open access links from 
to the list of external document links (if available).
Privacy notice: By enabling the option above, your browser will contact the API of unpaywall.org to load hyperlinks to open access articles. Although we do not have any reason to believe that your call will be tracked, we do not have any control over how the remote server uses your data. So please proceed with care and consider checking the Unpaywall privacy policy.
Archived links via Wayback Machine
For web page which are no longer available, try to retrieve content from the 
of the Internet Archive (if available).
Privacy notice: By enabling the option above, your browser will contact the API of archive.org to check for archived content of web pages that are no longer available. Although we do not have any reason to believe that your call will be tracked, we do not have any control over how the remote server uses your data. So please proceed with care and consider checking the Internet Archive privacy policy.
Reference lists
Add a list of references from 
, 
, and 
to record detail pages.
load references from crossref.org and opencitations.net
Privacy notice: By enabling the option above, your browser will contact the APIs of crossref.org, opencitations.net, and semanticscholar.org to load article reference information. Although we do not have any reason to believe that your call will be tracked, we do not have any control over how the remote server uses your data. So please proceed with care and consider checking the Crossref privacy policy and the OpenCitations privacy policy, as well as the AI2 Privacy Policy covering Semantic Scholar.
Citation data
Add a list of citing articles from and to record detail pages.
load citations from opencitations.net
Privacy notice: By enabling the option above, your browser will contact the API of opencitations.net and semanticscholar.org to load citation information. Although we do not have any reason to believe that your call will be tracked, we do not have any control over how the remote server uses your data. So please proceed with care and consider checking the OpenCitations privacy policy as well as the AI2 Privacy Policy covering Semantic Scholar.
OpenAlex data
Load additional information about publications from 
.
Privacy notice: By enabling the option above, your browser will contact the API of openalex.org to load additional information. Although we do not have any reason to believe that your call will be tracked, we do not have any control over how the remote server uses your data. So please proceed with care and consider checking the information given by OpenAlex.
last updated on 2024-06-26 23:16 CEST by the dblp team
all metadata released as open data under CC0 1.0 license
see also: Terms of Use | Privacy Policy | Imprint
dblp was originally created in 1993 at:
since 2018, dblp has been operated and maintained by:
the dblp computer science bibliography is funded and supported by:
