| [1] |
Zhiqiang Cai, Seokchan Kim, Sangdong Kim, and Sooryun Kong. A
finite element method using singular functions for Poisson
equations: mixed boundary conditions. Comput. Methods Appl.
Mech. Engrg., 195(19-22):2635-2648, 2006. |
| [2] |
Zhiqiang Cai and Xiu Ye. A mixed nonconforming finite element
for linear elasticity. Numer. Methods Partial Differential
Equations, 21(6):1043-1051, 2005. |
| [3] |
Zhiqiang Cai, Johannes Korsawe, and Gerhard Starke. An adaptive
least squares mixed finite element method for the
stress-displacement formulation of linear elasticity. Numer.
Methods Partial Differential Equations, 21(1):132-148,
2005. |
| [4] |
Zhiqiang Cai, Barry Lee, and Ping Wang. Least-squares methods
for incompressible Newtonian fluid flow: linear stationary
problems. SIAM J. Numer. Anal., 42(2):843-859
(electronic), 2004. |
| [5] |
Zhiqiang Cai and Gerhard Starke. Least-squares methods for
linear elasticity. SIAM J. Numer. Anal., 42(2):826-842
(electronic), 2004. |
| [6] |
Zhiqiang Cai and Gerhard Starke. First-order system least
squares for the stress-displacement formulation: linear elasticity.
SIAM J. Numer. Anal., 41(2):715-730 (electronic),
2003. |
| [7] |
Zhiqiang Cai, Jim Douglas, Jr., and 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. Challenges in computational mathematics (Pohang, 2001). |
| [8] |
Z. Cai, R. R. Parashkevov, T. F. Russell,
J. D. Wilson, and X. Ye. Domain decomposition for a mixed
finite element method in three dimensions. SIAM J. Numer.
Anal., 41(1):181-194 (electronic), 2003. |
| [9] |
Zhiqiang Cai, Seokchan Kim, and 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. Preconditioned robust iterative solution
methods, PRISM '01 (Nijmegen). |
| [10] |
Zhiqiang Cai and 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 (electronic), 2002. |
| [11] |
Z. Cai, T. A. Manteuffel, S. F. McCormick, and
J. Ruge. First-order system LL*
(FOSLL*): scalar elliptic partial differential equations.
SIAM J. Numer. Anal., 39(4):1418-1445 (electronic),
2001. |
| [12] |
Zhiqiang Cai, Seokchan Kim, and Byeong-Chun Shin. Solution
methods for the Poisson equation with corner singularities:
numerical results. SIAM J. Sci. Comput., 23(2):672-682
(electronic), 2001. Copper Mountain Conference (2000). |
| [13] |
Zhiqiang Cai and Seokchan Kim. A finite element method using
singular functions for the Poisson equation: corner singularities.
SIAM J. Numer. Anal., 39(1):286-299 (electronic),
2001. |
| [14] |
Zhiqiang Cai. Least squares for the perturbed Stokes equations
and the Reissner-Mindlin plate. SIAM J. Numer. Anal.,
38(5):1561-1581 (electronic), 2000. |
| [15] |
Z. Cai, J. Douglas, Jr., J. E. Santos,
D. Sheen, and X. Ye. Nonconforming quadrilateral finite
elements: a correction. Calcolo, 37(4):253-254, 2000. |
| [16] |
Z. Cai, C.-O. Lee, T. A. Manteuffel, and S. F.
McCormick. First-order system least squares for the Stokes and
linear elasticity equations: further results. SIAM J. Sci.
Comput., 21(5):1728-1739 (electronic), 2000. Iterative methods
for solving systems of algebraic equations (Copper Mountain, CO,
1998). |
| [17] |
Z. Cai, C.-O. Lee, T. A. Manteuffel, and S. F.
McCormick. First-order system least squares for linear elasticity:
numerical results. SIAM J. Sci. Comput., 21(5):1706-1727
(electronic), 2000. Iterative methods for solving systems of
algebraic equations (Copper Mountain, CO, 1998). |
| [18] |
Zhiqiang Cai and Xiu Ye. A least-squares finite element
approximation for the compressible Stokes equations. Numer.
Methods Partial Differential Equations, 16(1):62-70,
2000. |
| [19] |
Zhiqiang Cai, Jim Douglas, Jr., and Xiu Ye. A stable
nonconforming quadrilateral finite element method for the
stationary Stokes and Navier-Stokes equations. Calcolo,
36(4):215-232, 1999. |
| [20] |
Zhiqiang Cai, Xiu Ye, and Huilong Zhang. Least-squares finite
element approximations for the Reissner-Mindlin plate. Numer.
Linear Algebra Appl., 6(6):479-496, 1999. Iterative solution
methods for the elasticity equations in mechanics and biomechanics,
IMMB'98, Part 1 (Nijmegen). |
| [21] |
Thomas Y. Hou, Xiao-Hui Wu, and Zhiqiang Cai. Convergence
of a multiscale finite element method for elliptic problems with
rapidly oscillating coefficients. Math. Comp.,
68(227):913-943, 1999. |
| [22] |
Zhiqiang Cai and Jim Douglas, Jr. Stabilized finite element
methods with fast iterative solution algorithms for the Stokes
problem. Comput. Methods Appl. Mech. Engrg.,
166(1-2):115-129, 1998. |
| [23] |
P. Bochev, Z. Cai, T. A. Manteuffel, and
S. F. McCormick. Analysis of velocity-flux first-order system
least-squares principles for the Navier-Stokes equations. I.
SIAM J. Numer. Anal., 35(3):990-1009 (electronic),
1998. |
| [24] |
Zhiqiang Cai, Thomas A. Manteuffel, Stephen F.
McCormick, and Seymour V. Parter. First-order system least
squares (FOSLS) for planar linear elasticity: pure traction
problem. SIAM J. Numer. Anal., 35(1):320-335 (electronic),
1998. |
| [25] |
Z. Cai, J. E. Jones, S. F. McCormick, and
T. F. Russell. Control-volume mixed finite element methods.
Comput. Geosci., 1(3-4):289-315 (1998), 1997. |
| [26] |
Z. Cai, T. A. Manteuffel, and S. F. McCormick.
First-order system least squares for the Stokes equations, with
application to linear elasticity. SIAM J. Numer. Anal.,
34(5):1727-1741, 1997. |
| [27] |
Zhiqiang Cai, Jan Mandel, and Steve McCormick. Multigrid
methods for nearly singular linear equations and eigenvalue
problems. SIAM J. Numer. Anal., 34(1):178-200, 1997. |
| [28] |
Zhiqiang Cai, Thomas A. Manteuffel, and Stephen F.
McCormick. First-order system least squares for second-order
partial differential equations. II. SIAM J. Numer. Anal.,
34(2):425-454, 1997. |
| [29] |
Zhiqiang Cai and 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. |
| [30] |
Zhiqiang Cai, Thomas A. Manteuffel, and Stephen F.
McCormick. First-order system least squares for
velocity-vorticity-pressure form of the Stokes equations, with
application to linear elasticity. Electron. Trans. Numer.
Anal., 3(Dec.):150-159 (electronic), 1995. |
| [31] |
Z. Cai, R. Lazarov, T. A. Manteuffel, and
S. F. McCormick. First-order system least squares for
second-order partial differential equations. I. SIAM J. Numer.
Anal., 31(6):1785-1799, 1994. |
| [32] |
Zhi Qiang Cai, Charles I. Goldstein, and
Joseph E. Pasciak. Multilevel iteration for mixed finite
element systems with penalty. SIAM J. Sci. Comput.,
14(5):1072-1088, 1993. |
| [33] |
Zhi Qiang Cai. Norm estimates of product operators with
application to domain decomposition. Appl. Math. Comput.,
53(2-3):251-276, 1993. |
| [34] |
Zhi Qiang Cai and Weinan E. Hierarchical method for
elliptic problems using wavelet. Comm. Appl. Numer.
Methods, 8(11):819-825, 1992. |
| [35] |
Zhi Qiang Cai. On the finite volume element method.
Numer. Math., 58(7):713-735, 1991. |
| [36] |
Zhi Qiang Cai, Jan Mandel, and Steve McCormick. The finite
volume element method for diffusion equations on general
triangulations. SIAM J. Numer. Anal., 28(2):392-402,
1991. |
| [37] |
Zhi Qiang Cai and Steve McCormick. On the accuracy of the
finite volume element method for diffusion equations on composite
grids. SIAM J. Numer. Anal., 27(3):636-655, 1990. |
| [38] |
Zhi Qiang Cai and Benju Guo. Error estimates for a Schwarz
alternating procedure on L-shaped regions. Appl. Math.
Comput., 28(1):39-46, 1988. |
| [39] |
Zhi Qiang Cai. The multigrid method with correction
procedure. J. Comput. Math., 5(4):336-341, 1987. |
| [40] |
Neng Chao Wang and Zhi Qiang Cai. The revised MGE
method. Numer. Math. J. Chinese Univ., 9(3):227-234,
1987. |
| [41] |
Zhi Qiang Cai, Neng Chao Wang, and Li Shan Kang.
The MGE method for elliptic boundary value problems. Math.
Numer. Sinica, 8(1):82-89, 1986. |
