Cai, Ying; Chen, Jinru; Wang, Nan A Nitsche mixed extended finite element method for the biharmonic interface problem. (English) Zbl 07594628 Math. Comput. Simul. 203, 112-130 (2023). MSC: 65-XX 74-XX PDF BibTeX XML Cite \textit{Y. Cai} et al., Math. Comput. Simul. 203, 112--130 (2023; Zbl 07594628) Full Text: DOI OpenURL
Peng, Na; Wang, Caiqun; An, Jing An efficient finite-element method and error analysis for the fourth-order elliptic equation in a circular domain. (English) Zbl 07579662 Int. J. Comput. Math. 99, No. 9, 1785-1802 (2022). MSC: 65N30 65N35 PDF BibTeX XML Cite \textit{N. Peng} et al., Int. J. Comput. Math. 99, No. 9, 1785--1802 (2022; Zbl 07579662) Full Text: DOI OpenURL
Du, Shaohong; Lin, Runchang; Zhang, Zhimin Residual-based a posteriori error estimators for mixed finite element methods for fourth order elliptic singularly perturbed problems. (English) Zbl 1493.65196 J. Comput. Appl. Math. 412, Article ID 114323, 16 p. (2022). MSC: 65N30 65N15 35B25 35J30 74K20 PDF BibTeX XML Cite \textit{S. Du} et al., J. Comput. Appl. Math. 412, Article ID 114323, 16 p. (2022; Zbl 1493.65196) Full Text: DOI OpenURL
Song, Shicang; Lu, Lijuan A nonconforming scheme with piecewise quasi three degree polynomial space to solve biharmonic problem. (English) Zbl 1475.65202 J. Appl. Math. Comput. 66, No. 1-2, 581-597 (2021). MSC: 65N30 PDF BibTeX XML Cite \textit{S. Song} and \textit{L. Lu}, J. Appl. Math. Comput. 66, No. 1--2, 581--597 (2021; Zbl 1475.65202) Full Text: DOI OpenURL
Zhang, Shuo An optimal piecewise cubic nonconforming finite element scheme for the planar biharmonic equation on general triangulations. (English) Zbl 1477.65251 Sci. China, Math. 64, No. 11, 2579-2602 (2021). MSC: 65N30 65N50 65N12 76E25 76W05 35Q35 PDF BibTeX XML Cite \textit{S. Zhang}, Sci. China, Math. 64, No. 11, 2579--2602 (2021; Zbl 1477.65251) Full Text: DOI arXiv OpenURL
Tang, Shibing; Xu, Xuejun An optimal multilevel method with one smoothing step for the Morley element. (English) Zbl 1473.65318 Comput. Methods Appl. Math. 21, No. 3, 609-633 (2021). MSC: 65N30 65N55 35J40 PDF BibTeX XML Cite \textit{S. Tang} and \textit{X. Xu}, Comput. Methods Appl. Math. 21, No. 3, 609--633 (2021; Zbl 1473.65318) Full Text: DOI OpenURL
Cai, Ying; Chen, Jinru; Wang, Nan A Nitsche extended finite element method for the biharmonic interface problem. (English) Zbl 07415034 Comput. Methods Appl. Mech. Eng. 382, Article ID 113880, 24 p. (2021). MSC: 65-XX 74-XX PDF BibTeX XML Cite \textit{Y. Cai} et al., Comput. Methods Appl. Mech. Eng. 382, Article ID 113880, 24 p. (2021; Zbl 07415034) Full Text: DOI OpenURL
Danumjaya, P.; Pany, Ambit Kumar; Pani, Amiya K. Morley FEM for the fourth-order nonlinear reaction-diffusion problems. (English) Zbl 07411571 Comput. Math. Appl. 99, 229-245 (2021). MSC: 65N30 65N15 35J40 65N12 65M15 PDF BibTeX XML Cite \textit{P. Danumjaya} et al., Comput. Math. Appl. 99, 229--245 (2021; Zbl 07411571) Full Text: DOI OpenURL
Li, Chong-Jun; Jia, Yan-Mei A superconvergent nonconforming quadrilateral spline element for biharmonic equation using the B-net method. (English) Zbl 1449.65318 Comput. Appl. Math. 39, No. 2, Paper No. 70, 31 p. (2020). MSC: 65N30 65D07 65N12 65N15 PDF BibTeX XML Cite \textit{C.-J. Li} and \textit{Y.-M. Jia}, Comput. Appl. Math. 39, No. 2, Paper No. 70, 31 p. (2020; Zbl 1449.65318) Full Text: DOI OpenURL
Li, Huiyuan; Shan, Weikun; Zhang, Zhimin \(C^1\)-conforming quadrilateral spectral element method for fourth-order equations. (English) Zbl 1449.65334 Commun. Appl. Math. Comput. 1, No. 3, 403-434 (2019). MSC: 65N35 41A10 PDF BibTeX XML Cite \textit{H. Li} et al., Commun. Appl. Math. Comput. 1, No. 3, 403--434 (2019; Zbl 1449.65334) Full Text: DOI OpenURL
Bao, Yuan; Meng, Zhaoliang; Luo, Zhongxuan A \(C^{0}\)-nonconforming quadrilateral finite element for the fourth-order elliptic singular perturbation problem. (English) Zbl 1426.65169 ESAIM, Math. Model. Numer. Anal. 52, No. 5, 1981-2001 (2018). Reviewer: Kai Schneider (Marseille) MSC: 65N30 65N12 35J30 35B25 PDF BibTeX XML Cite \textit{Y. Bao} et al., ESAIM, Math. Model. Numer. Anal. 52, No. 5, 1981--2001 (2018; Zbl 1426.65169) Full Text: DOI OpenURL
Zhao, Jikun; Zhang, Bei; Chen, Shaochun; Mao, Shipeng The Morley-type virtual element for plate bending problems. (English) Zbl 1397.65299 J. Sci. Comput. 76, No. 1, 610-629 (2018). MSC: 65N30 65N12 74K20 74S05 PDF BibTeX XML Cite \textit{J. Zhao} et al., J. Sci. Comput. 76, No. 1, 610--629 (2018; Zbl 1397.65299) Full Text: DOI OpenURL
Chen, Zhiming; Tuo, Rui; Zhang, Wenlong Stochastic convergence of a nonconforming finite element method for the thin plate spline smoother for observational data. (English) Zbl 1397.65254 SIAM J. Numer. Anal. 56, No. 2, 635-659 (2018). Reviewer: Calin Ioan Gheorghiu (Cluj-Napoca) MSC: 65N30 65N15 PDF BibTeX XML Cite \textit{Z. Chen} et al., SIAM J. Numer. Anal. 56, No. 2, 635--659 (2018; Zbl 1397.65254) Full Text: DOI arXiv OpenURL
Zhao, Jikun; Chen, Shaochun; Zhang, Bei The nonconforming virtual element method for plate bending problems. (English) Zbl 1396.74098 Math. Models Methods Appl. Sci. 26, No. 9, 1671-1687 (2016). MSC: 74S05 65N30 65N12 74K20 PDF BibTeX XML Cite \textit{J. Zhao} et al., Math. Models Methods Appl. Sci. 26, No. 9, 1671--1687 (2016; Zbl 1396.74098) Full Text: DOI OpenURL
Zhang, Shuo Stable finite element pair for Stokes problem and discrete Stokes complex on quadrilateral grids. (English) Zbl 1381.76208 Numer. Math. 133, No. 2, 371-408 (2016). MSC: 76M10 65N30 65N12 76D07 PDF BibTeX XML Cite \textit{S. Zhang}, Numer. Math. 133, No. 2, 371--408 (2016; Zbl 1381.76208) Full Text: DOI arXiv OpenURL
An, Jing; Luo, Zhendong A high accuracy spectral method based on \(\min\)/\(\max\) principle for biharmonic eigenvalue problems on a spherical domain. (English) Zbl 1336.65185 J. Math. Anal. Appl. 439, No. 1, 385-395 (2016). MSC: 65N25 35P15 65N15 65N35 65N30 PDF BibTeX XML Cite \textit{J. An} and \textit{Z. Luo}, J. Math. Anal. Appl. 439, No. 1, 385--395 (2016; Zbl 1336.65185) Full Text: DOI OpenURL
Luo, Zhendong A high accuracy numerical method based on spectral theory of compact operator for biharmonic eigenvalue equations. (English) Zbl 1331.65164 J. Inequal. Appl. 2016, Paper No. 77, 11 p. (2016). MSC: 65N35 65N30 PDF BibTeX XML Cite \textit{Z. Luo}, J. Inequal. Appl. 2016, Paper No. 77, 11 p. (2016; Zbl 1331.65164) Full Text: DOI OpenURL
Xie, Pingli; Hu, Meng Convergence analysis of incomplete biquadratic rectangular element for fourth-order singular perturbation problem on anisotropic meshes. (English) Zbl 1470.74064 Abstr. Appl. Anal. 2014, Article ID 234375, 11 p. (2014). MSC: 74S05 65N30 65N15 PDF BibTeX XML Cite \textit{P. Xie} and \textit{M. Hu}, Abstr. Appl. Anal. 2014, Article ID 234375, 11 p. (2014; Zbl 1470.74064) Full Text: DOI OpenURL
Andreev, Andrey; Racheva, Milena Two-sided bounds of eigenvalues of second- and fourth-order elliptic operators. (English) Zbl 1340.65256 Appl. Math., Praha 59, No. 4, 371-390 (2014). MSC: 65N25 65N30 35P15 74K20 74S05 PDF BibTeX XML Cite \textit{A. Andreev} and \textit{M. Racheva}, Appl. Math., Praha 59, No. 4, 371--390 (2014; Zbl 1340.65256) Full Text: DOI Link OpenURL
Li, Mingxia; Guan, Xiaofei; Mao, Shipeng New error estimates of the Morley element for the plate bending problems. (English) Zbl 1301.74046 J. Comput. Appl. Math. 263, 405-416 (2014). MSC: 74S05 74G60 74K20 65N15 65N30 PDF BibTeX XML Cite \textit{M. Li} et al., J. Comput. Appl. Math. 263, 405--416 (2014; Zbl 1301.74046) Full Text: DOI OpenURL
Meng, Zhaoliang; Sheen, Dongwoo; Luo, Zhongxuan; Kim, Sihwan Three-dimensional quadratic nonconforming brick element. (English) Zbl 1355.65158 Numer. Methods Partial Differ. Equations 30, No. 1, 158-174 (2014). MSC: 65N30 65N15 PDF BibTeX XML Cite \textit{Z. Meng} et al., Numer. Methods Partial Differ. Equations 30, No. 1, 158--174 (2014; Zbl 1355.65158) Full Text: DOI arXiv OpenURL
Chen, Hong-Ru; Chen, Shao-Chun; Qiao, Zhong-Hua \(C^0\)-nonconforming triangular prism elements for the three-dimensional fourth-order elliptic problem. (English) Zbl 1269.65122 J. Sci. Comput. 55, No. 3, 645-658 (2013). Reviewer: Abdallah Bradji (Annaba) MSC: 65N30 65N15 65N12 35J40 PDF BibTeX XML Cite \textit{H.-R. Chen} et al., J. Sci. Comput. 55, No. 3, 645--658 (2013; Zbl 1269.65122) Full Text: DOI OpenURL
Park, Chunjae; Sheen, Dongwoo A quadrilateral Morley element for biharmonic equations. (English) Zbl 1316.74063 Numer. Math. 124, No. 2, 395-413 (2013). MSC: 74S05 65N30 PDF BibTeX XML Cite \textit{C. Park} and \textit{D. Sheen}, Numer. Math. 124, No. 2, 395--413 (2013; Zbl 1316.74063) Full Text: DOI OpenURL
Wang, Li; Wu, Yongke; Xie, Xiaoping Uniformly stable rectangular elements for fourth order elliptic singular perturbation problems. (English) Zbl 1307.65170 Numer. Methods Partial Differ. Equations 29, No. 3, 721-737 (2013). Reviewer: Yaşar Sözen (Ankara) MSC: 65N30 65N12 35J40 35B25 PDF BibTeX XML Cite \textit{L. Wang} et al., Numer. Methods Partial Differ. Equations 29, No. 3, 721--737 (2013; Zbl 1307.65170) Full Text: DOI arXiv OpenURL
Wang, Ming; Xu, Jinchao Minimal finite element spaces for \(2m\)-th-order partial differential equations in \(\mathbb{R}^n\). (English) Zbl 1264.65199 Math. Comput. 82, No. 281, 25-43 (2013). Reviewer: Abdallah Bradji (Annaba) MSC: 65N30 65N15 35J05 35J40 65N12 PDF BibTeX XML Cite \textit{M. Wang} and \textit{J. Xu}, Math. Comput. 82, No. 281, 25--43 (2013; Zbl 1264.65199) Full Text: DOI OpenURL
Hu, Jun; Huang, Yunqing; Shen, Quan A high accuracy post-processing algorithm for the eigenvalues of elliptic operators. (English) Zbl 1255.65206 J. Sci. Comput. 52, No. 2, 426-445 (2012). MSC: 65N25 PDF BibTeX XML Cite \textit{J. Hu} et al., J. Sci. Comput. 52, No. 2, 426--445 (2012; Zbl 1255.65206) Full Text: DOI OpenURL
Guzmán, Johnny; Leykekhman, Dmitriy; Neilan, Michael A family of non-conforming elements and the analysis of Nitsche’s method for a singularly perturbed fourth order problem. (English) Zbl 1253.65150 Calcolo 49, No. 2, 95-125 (2012). MSC: 65M60 65N12 34D15 PDF BibTeX XML Cite \textit{J. Guzmán} et al., Calcolo 49, No. 2, 95--125 (2012; Zbl 1253.65150) Full Text: DOI OpenURL
Yang, Yidu; Lin, Qun; Bi, Hai; Li, Qin Eigenvalue approximations from below using Morley elements. (English) Zbl 1253.65181 Adv. Comput. Math. 36, No. 3, 443-450 (2012). MSC: 65N25 65N30 PDF BibTeX XML Cite \textit{Y. Yang} et al., Adv. Comput. Math. 36, No. 3, 443--450 (2012; Zbl 1253.65181) Full Text: DOI OpenURL
Huang, Jianguo; Huang, Xuehai Local and parallel algorithms for fourth-order problems discretized by the Morley-Wang-Xu element method. (English) Zbl 1235.74285 Numer. Math. 119, No. 4, 667-697 (2011). Reviewer: Ivan Secrieru (Chişinău) MSC: 74S05 74K20 65N30 65N50 65Y05 PDF BibTeX XML Cite \textit{J. Huang} and \textit{X. Huang}, Numer. Math. 119, No. 4, 667--697 (2011; Zbl 1235.74285) Full Text: DOI OpenURL
Feng, Xiaobing; Neilan, Michael Discontinuous finite element methods for a bi-wave equation modeling \(d\)-wave superconductors. (English) Zbl 1222.82085 Math. Comput. 80, No. 275, 1303-1333 (2011). Reviewer: Vicenţiu D. Rădulescu (Craiova) MSC: 82D55 82-08 35Q56 65N30 65N12 65N15 PDF BibTeX XML Cite \textit{X. Feng} and \textit{M. Neilan}, Math. Comput. 80, No. 275, 1303--1333 (2011; Zbl 1222.82085) Full Text: DOI OpenURL
Beirão da Veiga, L.; Niiranen, J.; Stenberg, R. A posteriori error analysis for the Morley plate element with general boundary conditions. (English) Zbl 1193.74162 Int. J. Numer. Methods Eng. 83, No. 1, 1-26 (2010). MSC: 74S05 74K20 65N15 65N30 PDF BibTeX XML Cite \textit{L. Beirão da Veiga} et al., Int. J. Numer. Methods Eng. 83, No. 1, 1--26 (2010; Zbl 1193.74162) Full Text: DOI Link OpenURL
Lai, Junjiang; Huang, Jianguo; Shi, Zhongci A lumped mass finite element method for vibration analysis of elastic plate-plate structures. (English) Zbl 1214.74014 Sci. China, Math. 53, No. 6, 1453-1474 (2010). MSC: 74S05 74H45 65M15 65M60 70J35 70J50 PDF BibTeX XML Cite \textit{J. Lai} et al., Sci. China, Math. 53, No. 6, 1453--1474 (2010; Zbl 1214.74014) Full Text: DOI OpenURL
Neilan, Michael A nonconforming Morley finite element method for the fully nonlinear Monge-Ampère equation. (English) Zbl 1201.65209 Numer. Math. 115, No. 3, 371-394 (2010). Reviewer: Pavel Burda (Praha) MSC: 65N30 65N12 35J60 PDF BibTeX XML Cite \textit{M. Neilan}, Numer. Math. 115, No. 3, 371--394 (2010; Zbl 1201.65209) Full Text: DOI OpenURL
Lang, Feng-Gong; Wang, Ren-Hong On the dimension of bivariate weak spline space over regular rectilinear partition. (English) Zbl 1194.41018 Result. Math. 57, No. 1-2, 79-95 (2010). Reviewer: H. P. Dikshit (Bhopal) MSC: 41A15 PDF BibTeX XML Cite \textit{F.-G. Lang} and \textit{R.-H. Wang}, Result. Math. 57, No. 1--2, 79--95 (2010; Zbl 1194.41018) Full Text: DOI OpenURL
Mao, Shipeng; Shi, Zhongci High-accuracy analysis of two nonconforming plate elements. (English) Zbl 1155.74045 Numer. Math. 111, No. 3, 407-443 (2009). MSC: 74S05 74K20 65N30 65N15 PDF BibTeX XML Cite \textit{S. Mao} and \textit{Z. Shi}, Numer. Math. 111, No. 3, 407--443 (2009; Zbl 1155.74045) Full Text: DOI OpenURL
Yang, Yidu; Chen, Zhen The order-preserving convergence for spectral approximation of self-adjoint completely continuous operators. (English) Zbl 1153.65055 Sci. China, Ser. A 51, No. 7, 1232-1242 (2008). Reviewer: Jiří Vaníček (Praha) MSC: 65J10 47A10 65N25 65N30 35P15 65N12 47F05 PDF BibTeX XML Cite \textit{Y. Yang} and \textit{Z. Chen}, Sci. China, Ser. A 51, No. 7, 1232--1242 (2008; Zbl 1153.65055) Full Text: DOI OpenURL
Chen, Shaochun; Yin, Li; Mao, Shipeng An anisotropic, superconvergent nonconforming plate finite element. (English) Zbl 1149.65091 J. Comput. Appl. Math. 220, No. 1-2, 96-110 (2008). Reviewer: Nicolae Pop (Baia Mare) MSC: 65N30 35J25 65N12 65N15 PDF BibTeX XML Cite \textit{S. Chen} et al., J. Comput. Appl. Math. 220, No. 1--2, 96--110 (2008; Zbl 1149.65091) Full Text: DOI OpenURL
Huang, Jianguo; Guo, Ling; Shi, Zhongci Vibration analysis of Kirchhoff plates by the Morley element method. (English) Zbl 1129.74046 J. Comput. Appl. Math. 213, No. 1, 14-34 (2008). MSC: 74S05 74H45 74K20 74H15 PDF BibTeX XML Cite \textit{J. Huang} et al., J. Comput. Appl. Math. 213, No. 1, 14--34 (2008; Zbl 1129.74046) Full Text: DOI OpenURL
Ming, Wang; Xu, Jinchao Nonconforming tetrahedral finite elements for fourth order elliptic equations. (English) Zbl 1125.65105 Math. Comput. 76, No. 257, 1-18 (2007). Reviewer: Viorel Arnăutu (Iaşi) MSC: 65N30 35J40 PDF BibTeX XML Cite \textit{W. Ming} and \textit{J. Xu}, Math. Comput. 76, No. 257, 1--18 (2007; Zbl 1125.65105) Full Text: DOI OpenURL
Huang, Jianguo; Shi, Zhongci; Xu, Yifeng Finite element analysis for general elastic multi-structures. (English) Zbl 1102.74041 Sci. China, Ser. A 49, No. 1, 109-129 (2006). MSC: 74S05 74K99 65N15 65N30 PDF BibTeX XML Cite \textit{J. Huang} et al., Sci. China, Ser. A 49, No. 1, 109--129 (2006; Zbl 1102.74041) Full Text: DOI OpenURL
Shi, Zhongci Nonconforming finite element methods. (English) Zbl 1013.65121 J. Comput. Appl. Math. 149, No. 1, 221-225 (2002). MSC: 65N30 35J40 35J25 PDF BibTeX XML Cite \textit{Z. Shi}, J. Comput. Appl. Math. 149, No. 1, 221--225 (2002; Zbl 1013.65121) Full Text: DOI OpenURL
Bělík, Pavel; Brule, Timothy; Luskin, Mitchell On the numerical modeling of deformations of pressurized martensitic thin films. (English) Zbl 1062.74047 M2AN, Math. Model. Numer. Anal. 35, No. 3, 525-548 (2001). Reviewer: Nicolae Pop (Baia Mare) MSC: 74S05 74K35 74N05 74F05 PDF BibTeX XML Cite \textit{P. Bělík} et al., M2AN, Math. Model. Numer. Anal. 35, No. 3, 525--548 (2001; Zbl 1062.74047) Full Text: DOI Numdam EuDML OpenURL
Huang, Jianguo; Li, Likang; Chen, Jinru On mortar-type Morley element method for plate bending problem. (English) Zbl 1013.74066 Appl. Numer. Math. 37, No. 4, 519-533 (2001). MSC: 74S05 74K20 PDF BibTeX XML Cite \textit{J. Huang} et al., Appl. Numer. Math. 37, No. 4, 519--533 (2001; Zbl 1013.74066) Full Text: DOI OpenURL
Nilssen, Trygve K.; Tai, Xue-Cheng; Winther, Ragnar A robust nonconforming \(H^2\)-element. (English) Zbl 0965.65127 Math. Comput. 70, No. 234, 489-505 (2001). Reviewer: Z.Dżygadło (Warszawa) MSC: 65N30 65N12 65N15 35J40 35B25 35J70 PDF BibTeX XML Cite \textit{T. K. Nilssen} et al., Math. Comput. 70, No. 234, 489--505 (2001; Zbl 0965.65127) Full Text: DOI OpenURL
Brenner, Susanne C. Convergence of nonconforming multigrid methods without full elliptic regularity. (English) Zbl 0912.65099 Math. Comput. 68, No. 225, 25-53 (1999). Reviewer: M.Bernadou (Le Chesnay) MSC: 65N55 65N30 65N12 35J25 35J40 PDF BibTeX XML Cite \textit{S. C. Brenner}, Math. Comput. 68, No. 225, 25--53 (1999; Zbl 0912.65099) Full Text: DOI OpenURL
Gu, Jinsheng; Hu, Xiancheng Extension theorems for plate elements with applications. (English) Zbl 0894.73152 Math. Comput. 66, No. 220, 1375-1388 (1997). MSC: 74S05 74K20 65N30 PDF BibTeX XML Cite \textit{J. Gu} and \textit{X. Hu}, Math. Comput. 66, No. 220, 1375--1388 (1997; Zbl 0894.73152) Full Text: DOI OpenURL