TY - BOOK AU - Kinderlehrer, D. AU - Stampacchia, G. PY - 2000 DA - 2000// TI - An Introduction to Variational Inequalities and Their Applications PB - SIAM CY - Philadelphia UR - https://doi.org/10.1137/1.9780898719451 DO - 10.1137/1.9780898719451 ID - Kinderlehrer2000 ER - TY - BOOK AU - Rodrigues, J. F. PY - 1987 DA - 1987// TI - Obstacle Problems in Mathematical Physics PB - North-Holland CY - Amsterdam ID - Rodrigues1987 ER - TY - JOUR AU - Brezzi, F. AU - Hager, W. W. AU - Raviart, P. A. PY - 1977 DA - 1977// TI - Error estimates for the finite element solution of variational inequalities JO - Numer. Math. VL - 28 UR - https://doi.org/10.1007/BF01404345 DO - 10.1007/BF01404345 ID - Brezzi1977 ER - TY - BOOK AU - Glowinski, R. AU - Lions, J. L. AU - Tremolieres, R. PY - 1981 DA - 1981// TI - Numerical Analysis of Variational Inequalities PB - North-Holland CY - Amsterdam ID - Glowinski1981 ER - TY - JOUR AU - Wang, L. H. PY - 2003 DA - 2003// TI - On the error estimate of nonconforming finite element approximation to the obstacle problem JO - J. Comput. Math. VL - 21 ID - Wang2003 ER - TY - JOUR AU - Li, M. X. AU - Lin, Q. AU - Zhang, S. H. PY - 2008 DA - 2008// TI - Superconvergence of finite element method for the Signorini problem JO - J. Comput. Appl. Math. VL - 222 UR - https://doi.org/10.1016/j.cam.2007.10.058 DO - 10.1016/j.cam.2007.10.058 ID - Li2008 ER - TY - JOUR AU - Shi, D. Y. AU - Ren, J. C. AU - Gong, W. PY - 2012 DA - 2012// TI - Convergence and superconvergence analysis of a nonconforming finite element method for solving the Signorini problem JO - Nonlinear Anal., Theory Methods Appl. VL - 75 UR - https://doi.org/10.1016/j.na.2012.01.007 DO - 10.1016/j.na.2012.01.007 ID - Shi2012 ER - TY - JOUR AU - Shi, D. Y. AU - Xu, C. PY - 2012 DA - 2012// TI - EQ1rot$EQ^{\mathrm{rot}}_{1}$ Nonconforming finite element approximation to Signorini problem JO - Sci. China Math. VL - 56 UR - https://doi.org/10.1007/s11425-013-4615-z DO - 10.1007/s11425-013-4615-z ID - Shi2012 ER - TY - JOUR AU - Shi, D. Y. AU - Wang, C. X. AU - Tang, Q. L. PY - 2015 DA - 2015// TI - Anisotropic Crouzeix-Raviart type nonconforming finite element methods to variational inequality problem with displacement obstacle JO - J. Comput. Math. VL - 33 UR - https://doi.org/10.4208/jcm.1406-m4309 DO - 10.4208/jcm.1406-m4309 ID - Shi2015 ER - TY - JOUR AU - Frehse, J. PY - 1973 DA - 1973// TI - On the regularity of the solution of the biharmonic variational inequality JO - Manuscr. Math. VL - 9 UR - https://doi.org/10.1007/BF01320669 DO - 10.1007/BF01320669 ID - Frehse1973 ER - TY - JOUR AU - Schild, B. PY - 1984 DA - 1984// TI - A regularity result for polyharmonic variational inequalities with thin obstacles JO - Ann. Sc. Norm. Super. Pisa, Cl. Sci. VL - 11 ID - Schild1984 ER - TY - JOUR AU - Caffarelli, L. A. AU - Friedman, A. AU - Torelli, A. PY - 1982 DA - 1982// TI - The two-obstacle problem for the biharmonic operator JO - Pac. J. Math. VL - 103 UR - https://doi.org/10.2140/pjm.1982.103.325 DO - 10.2140/pjm.1982.103.325 ID - Caffarelli1982 ER - TY - JOUR AU - Wang, L. H. PY - 1990 DA - 1990// TI - Some nonconforming finite element approximations of a fourth order variational inequality with displacement obstacle JO - Acta Numer. Math. VL - 12 ID - Wang1990 ER - TY - JOUR AU - Wang, L. H. PY - 1992 DA - 1992// TI - Some strongly discontinuous nonconforming finite element approximations of a fourth order variational inequality with displacement obstacle JO - Acta Numer. Math. VL - 14 ID - Wang1992 ER - TY - JOUR AU - Shi, D. Y. AU - Chen, S. C. PY - 2003 DA - 2003// TI - Quasi-conforming element approximation for a fourth order variational inequality with displacement obstacle JO - Acta Math. Sci., Ser. B VL - 23 ID - Shi2003 ER - TY - JOUR AU - Shi, D. Y. AU - Chen, S. C. PY - 2003 DA - 2003// TI - General estimates on nonconforming elements for a fourth order variational problem JO - Math. Numer. Sin. VL - 25 ID - Shi2003 ER - TY - JOUR AU - Brenner, S. C. AU - Sung, L. -. Y. AU - Zhang, Y. PY - 2012 DA - 2012// TI - Finite element methods for the displacement obstacle problem of clamped plates JO - Math. Comput. VL - 81 UR - https://doi.org/10.1090/S0025-5718-2012-02602-0 DO - 10.1090/S0025-5718-2012-02602-0 ID - Brenner2012 ER - TY - JOUR AU - Brenner, S. C. AU - Sung, L. -. Y. AU - Zhang, H. C. AU - Zhang, Y. PY - 2013 DA - 2013// TI - A Morley finite element method for the displacement obstacle problem of clamped Kirchhoff plates JO - J. Comput. Appl. Math. VL - 254 UR - https://doi.org/10.1016/j.cam.2013.02.028 DO - 10.1016/j.cam.2013.02.028 ID - Brenner2013 ER - TY - STD TI - Brenner, SC, Christopher, BD, Sung, L-Y: A generalized finite element method for the displacement obstacle problem of clamped Kirchhoff plates (2012). arXiv:1212.3026 UR - http://arxiv.org/abs/arXiv:1212.3026 ID - ref19 ER - TY - JOUR AU - Brenner, S. C. AU - Sung, L. -. Y. AU - Zhang, H. C. AU - Zhang, Y. PY - 2012 DA - 2012// TI - A quadratic C0$C^{0}$ interior penalty method for the displacement obstacle problem of clamped Kirchhoff plates JO - SIAM J. Numer. Anal. VL - 50 UR - https://doi.org/10.1137/110845926 DO - 10.1137/110845926 ID - Brenner2012 ER - TY - JOUR AU - Argyris, J. H. AU - Fried, I. AU - Scharpf, D. W. PY - 1968 DA - 1968// TI - The TUBA family of plate elements for the matrix displacement method JO - Aeronaut. J. R. Aeronaut. Soc. VL - 72 ID - Argyris1968 ER - TY - CHAP AU - Bogner, F. K. AU - Fox, R. L. AU - Schmit, L. A. PY - 1965 DA - 1965// TI - The generation of interelement compatible stiffness and mass matrices by the use of interpolation formulas BT - Proceedings of the Conference on Matrix Methods in Structural Mechanics ID - Bogner1965 ER - TY - JOUR AU - Stummel, F. PY - 1979 DA - 1979// TI - The generalized patch test JO - SIAM J. Numer. Anal. VL - 16 UR - https://doi.org/10.1137/0716037 DO - 10.1137/0716037 ID - Stummel1979 ER - TY - JOUR AU - Shi, Z. C. PY - 1987 DA - 1987// TI - The F-E-M-test for convergence of nonconforming finite element JO - Math. Comput. VL - 49 ID - Shi1987 ER - TY - JOUR AU - Veubeke, F. D. PY - 1974 DA - 1974// TI - Variational principles and the patch test JO - Int. J. Numer. Methods Eng. VL - 8 UR - https://doi.org/10.1002/nme.1620080408 DO - 10.1002/nme.1620080408 ID - Veubeke1974 ER - TY - BOOK AU - Ciarlet, P. G. PY - 1978 DA - 1978// TI - The Finite Element Method for Elliptic Problems PB - North-Holland CY - Amsterdam ID - Ciarlet1978 ER - TY - JOUR AU - Lascaux, P. AU - Lesaint, P. PY - 1975 DA - 1975// TI - Some nonconforming finite elements for the plate bending problem JO - Rev. Fr. Autom. Inform. Rech. Opér. , Anal. Numér. VL - 9 ID - Lascaux1975 ER - TY - JOUR AU - Shi, Z. C. PY - 1984 DA - 1984// TI - The generalized patch test for Zienkiewicz’s triangle JO - J. Comput. Math. VL - 2 ID - Shi1984 ER - TY - JOUR AU - Chen, S. C. AU - Shi, Z. C. PY - 1991 DA - 1991// TI - Double set parameter method of constructing stiffness matrices JO - Math. Numer. Sin. VL - 15 ID - Chen1991 ER - TY - STD TI - Shi, DY: Research on nonconforming finite element problems. PhD thesis, Xi’an JiaoTong University, Xi’an (1997) ID - ref30 ER - TY - JOUR AU - Chen, S. C. AU - Li, Y. AU - Mao, S. P. PY - 2008 DA - 2008// TI - An anisotropic, superconvergent nonconforming plate finite element JO - J. Comput. Appl. Math. VL - 220 UR - https://doi.org/10.1016/j.cam.2007.07.034 DO - 10.1016/j.cam.2007.07.034 ID - Chen2008 ER - TY - JOUR AU - Chen, S. C. AU - Liu, M. F. AU - Qiao, Z. H. PY - 2010 DA - 2010// TI - An anisotropic nonconforming element for fourth order elliptic singular perturbation problem JO - Int. J. Numer. Anal. Model. VL - 7 ID - Chen2010 ER - TY - JOUR AU - Chen, S. C. AU - Zhao, Y. C. AU - Shi, D. Y. PY - 2005 DA - 2005// TI - Non-C0$C^{0}$ nonconforming elements for elliptic fourth order singular perturbation problem JO - J. Comput. Math. VL - 23 ID - Chen2005 ER - TY - JOUR AU - Mao, S. P. AU - Chen, S. C. AU - Sun, H. X. PY - 2006 DA - 2006// TI - A quadrilateral, anisotropic, superconvergent, nonconforming double set parameter element JO - Appl. Numer. Math. VL - 56 UR - https://doi.org/10.1016/j.apnum.2005.07.005 DO - 10.1016/j.apnum.2005.07.005 ID - Mao2006 ER - TY - JOUR AU - Shi, D. Y. AU - Xie, P. L. PY - 2010 DA - 2010// TI - A new robust C0$C^{0}$-type nonconforming triangular element for singular perturbation problems JO - Appl. Math. Comput. VL - 217 UR - https://doi.org/10.1016/j.amc.2010.06.047 DO - 10.1016/j.amc.2010.06.047 ID - Shi2010 ER - TY - JOUR AU - Shi, D. Y. AU - Xie, P. L. PY - 2011 DA - 2011// TI - A robust double set parameter nonconforming rectangular element for fourth order singular perturbation problems JO - Proc. Environ. Sci. VL - 10 UR - https://doi.org/10.1016/j.proenv.2011.09.138 DO - 10.1016/j.proenv.2011.09.138 ID - Shi2011 ER - TY - JOUR AU - Brenner, S. C. PY - 1996 DA - 1996// TI - A two-level additive Schwarz preconditioner for nonconforming plate elements JO - Numer. Math. VL - 72 UR - https://doi.org/10.1007/s002110050176 DO - 10.1007/s002110050176 ID - Brenner1996 ER - TY - JOUR AU - Morley, L. S. D. PY - 1968 DA - 1968// TI - The triangular equilibrium problem in the solution of plate bending problems JO - Aeronaut. Q. VL - 19 ID - Morley1968 ER - TY - BOOK AU - Zhang, H. Q. AU - Wang, M. PY - 1991 DA - 1991// TI - The Mathematical Theory of Finite Elements PB - Science Press CY - Beijing ID - Zhang1991 ER -