Carstensen, Carsten; Puttkammer, Sophie Adaptive guaranteed lower eigenvalue bounds with optimal convergence rates. (English) Zbl 07802480 Numer. Math. 156, No. 1, 1-38 (2024). Reviewer: Petr Sváček (Praha) MSC: 65N25 65N30 65N50 65N12 65N15 65Y20 PDFBibTeX XMLCite \textit{C. Carstensen} and \textit{S. Puttkammer}, Numer. Math. 156, No. 1, 1--38 (2024; Zbl 07802480) Full Text: DOI arXiv OA License
An, Qi; Huang, Xuehai; Zhang, Chao A decoupled finite element method for the triharmonic equation. (English) Zbl 07766546 Appl. Math. Lett. 147, Article ID 108843, 8 p. (2024). MSC: 65Nxx 35Jxx 41Axx PDFBibTeX XMLCite \textit{Q. An} et al., Appl. Math. Lett. 147, Article ID 108843, 8 p. (2024; Zbl 07766546) Full Text: DOI
Ye, Xiu; Zhang, Shangyou A conforming DG method for the biharmonic equation on polytopal meshes. (English) Zbl 07793828 Int. J. Numer. Anal. Model. 20, No. 6, 855-869 (2023). MSC: 65N15 65N30 76D07 PDFBibTeX XMLCite \textit{X. Ye} and \textit{S. Zhang}, Int. J. Numer. Anal. Model. 20, No. 6, 855--869 (2023; Zbl 07793828) Full Text: DOI arXiv
Chen, Chunyu; Huang, Xuehai; Wei, Huayi \(H^m\)-conforming virtual elements in arbitrary dimension. (English) Zbl 1514.65166 SIAM J. Numer. Anal. 60, No. 6, 3099-3123 (2022). MSC: 65N30 65N12 65N15 65N22 PDFBibTeX XMLCite \textit{C. Chen} et al., SIAM J. Numer. Anal. 60, No. 6, 3099--3123 (2022; Zbl 1514.65166) Full Text: DOI
Antonietti, Paola F.; Manzini, Gianmarco; Mazzieri, Ilario; Scacchi, Simone; Verani, Marco The conforming virtual element method for polyharmonic and elastodynamics problems: a review. (English) Zbl 1503.65215 Antonietti, Paola F. (ed.) et al., The virtual element method and its applications. Cham: Birkhäuser. SEMA SIMAI Springer Ser. 31, 411-451 (2022). MSC: 65M60 65M06 65N30 74B10 74R10 74S05 74S20 35Q74 PDFBibTeX XMLCite \textit{P. F. Antonietti} et al., SEMA SIMAI Springer Ser. 31, 411--451 (2022; Zbl 1503.65215) Full Text: DOI arXiv
Chen, Huangxin; Li, Jingzhi; Qiu, Weifeng A \(C^0\) interior penalty method for \(m\)th-Laplace equation. (English) Zbl 1503.65290 ESAIM, Math. Model. Numer. Anal. 56, No. 6, 2081-2103 (2022). MSC: 65N30 65N12 65N15 35J05 PDFBibTeX XMLCite \textit{H. Chen} et al., ESAIM, Math. Model. Numer. Anal. 56, No. 6, 2081--2103 (2022; Zbl 1503.65290) Full Text: DOI arXiv
Dassi, Franco; Velásquez, Iván Virtual element method on polyhedral meshes for bi-harmonic eigenvalues problems. (English) Zbl 1524.65785 Comput. Math. Appl. 121, 85-101 (2022). MSC: 65N30 65N25 65N15 65N12 74S05 31A30 74H45 35A15 65N35 PDFBibTeX XMLCite \textit{F. Dassi} and \textit{I. Velásquez}, Comput. Math. Appl. 121, 85--101 (2022; Zbl 1524.65785) Full Text: DOI
Ye, Xiu; Zhang, Shangyou A family of H-div-div mixed triangular finite elements for the biharmonic equation. (English) Zbl 1497.65240 Results Appl. Math. 15, Article ID 100318, 16 p. (2022). MSC: 65N30 65N15 65N12 PDFBibTeX XMLCite \textit{X. Ye} and \textit{S. Zhang}, Results Appl. Math. 15, Article ID 100318, 16 p. (2022; Zbl 1497.65240) Full Text: DOI
Boffi, Daniele (ed.); Carstensen, Carsten (ed.); Ern, Alexandre (ed.); Hu, Jun (ed.) Nonstandard finite element methods. Abstracts from the workshop held January 10–16, 2021 (hybrid meeting). (English) Zbl 1487.00033 Oberwolfach Rep. 18, No. 1, 87-148 (2021). MSC: 00B05 00B25 65-06 65N30 PDFBibTeX XMLCite \textit{D. Boffi} (ed.) et al., Oberwolfach Rep. 18, No. 1, 87--148 (2021; Zbl 1487.00033) Full Text: DOI
Carstensen, Carsten; Nataraj, Neela A priori and a posteriori error analysis of the Crouzeix-Raviart and Morley FEM with original and modified right-hand sides. (English) Zbl 1476.65294 Comput. Methods Appl. Math. 21, No. 2, 289-315 (2021). MSC: 65N30 65N12 65N15 65N50 PDFBibTeX XMLCite \textit{C. Carstensen} and \textit{N. Nataraj}, Comput. Methods Appl. Math. 21, No. 2, 289--315 (2021; Zbl 1476.65294) Full Text: DOI arXiv
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 PDFBibTeX XMLCite \textit{S. Zhang}, Sci. China, Math. 64, No. 11, 2579--2602 (2021; Zbl 1477.65251) Full Text: DOI arXiv
Huang, Xuehai; Shi, Yuling; Wang, Wenqing A Morley-Wang-Xu element method for a fourth order elliptic singular perturbation problem. (English) Zbl 1476.65302 J. Sci. Comput. 87, No. 3, Paper No. 84, 24 p. (2021). MSC: 65N30 65N12 65F08 65F10 35B25 35J30 35J05 76D07 76S05 76M10 PDFBibTeX XMLCite \textit{X. Huang} et al., J. Sci. Comput. 87, No. 3, Paper No. 84, 24 p. (2021; Zbl 1476.65302) Full Text: DOI arXiv
Zeng, Huilan; Zhang, Chen-Song; Zhang, Shuo Optimal quadratic element on rectangular grids for \(H^1\) problems. (English) Zbl 1472.65150 BIT 61, No. 2, 665-689 (2021). MSC: 65N30 65N25 65N12 65N15 65N22 35P15 PDFBibTeX XMLCite \textit{H. Zeng} et al., BIT 61, No. 2, 665--689 (2021; Zbl 1472.65150) Full Text: DOI arXiv
Huang, Jianguo; Yu, Yue A medius error analysis for nonconforming virtual element methods for Poisson and biharmonic equations. (English) Zbl 1457.65197 J. Comput. Appl. Math. 386, Article ID 113229, 21 p. (2021). Reviewer: Bülent Karasözen (Ankara) MSC: 65N30 65N15 35J05 31A30 35D30 PDFBibTeX XMLCite \textit{J. Huang} and \textit{Y. Yu}, J. Comput. Appl. Math. 386, Article ID 113229, 21 p. (2021; Zbl 1457.65197) Full Text: DOI
Xu, Jinchao Finite neuron method and convergence analysis. (English) Zbl 1473.65350 Commun. Comput. Phys. 28, No. 5, 1707-1745 (2020). MSC: 65N99 62M45 65N30 68T07 65N12 65N15 PDFBibTeX XMLCite \textit{J. Xu}, Commun. Comput. Phys. 28, No. 5, 1707--1745 (2020; Zbl 1473.65350) Full Text: DOI arXiv
Huang, Xuehai Nonconforming virtual element method for \(2m\)th order partial differential equations in \(\mathbb{R}^n\) with \(m>n\). (English) Zbl 1468.65192 Calcolo 57, No. 4, Paper No. 42, 38 p. (2020). MSC: 65N30 65N12 65N15 65N22 PDFBibTeX XMLCite \textit{X. Huang}, Calcolo 57, No. 4, Paper No. 42, 38 p. (2020; Zbl 1468.65192) Full Text: DOI arXiv
Antonietti, Paola F.; Manzini, G.; Verani, Marco The conforming virtual element method for polyharmonic problems. (English) Zbl 1452.65320 Comput. Math. Appl. 79, No. 7, 2021-2034 (2020). MSC: 65N30 65N12 31A30 35J05 PDFBibTeX XMLCite \textit{P. F. Antonietti} et al., Comput. Math. Appl. 79, No. 7, 2021--2034 (2020; Zbl 1452.65320) Full Text: DOI arXiv
Beirão da Veiga, Lourenco; Dassi, Franco; Russo, Alessandro A \(C^1\) virtual element method on polyhedral meshes. (English) Zbl 1454.65161 Comput. Math. Appl. 79, No. 7, 1936-1955 (2020). MSC: 65N30 65N12 PDFBibTeX XMLCite \textit{L. Beirão da Veiga} et al., Comput. Math. Appl. 79, No. 7, 1936--1955 (2020; Zbl 1454.65161) Full Text: DOI arXiv
Hu, Jun; Tian, Shudan; Zhang, Shangyou A family of 3D \(H^2\)-nonconforming tetrahedral finite elements for the biharmonic equation. (English) Zbl 1446.65171 Sci. China, Math. 63, No. 8, 1505-1522 (2020). MSC: 65N30 65N15 31A30 PDFBibTeX XMLCite \textit{J. Hu} et al., Sci. China, Math. 63, No. 8, 1505--1522 (2020; Zbl 1446.65171) Full Text: DOI arXiv
Chen, Long; Huang, Xuehai Nonconforming virtual element method for \(2m\) th order partial differential equations in \(\mathbb{R}^n\). (English) Zbl 1436.65175 Math. Comput. 89, No. 324, 1711-1744 (2020). MSC: 65N30 65N12 65N22 65N15 PDFBibTeX XMLCite \textit{L. Chen} and \textit{X. Huang}, Math. Comput. 89, No. 324, 1711--1744 (2020; Zbl 1436.65175) Full Text: DOI arXiv
Sorokina, Tatyana; Zhang, Shangyou Conforming and nonconforming harmonic finite elements. (English) Zbl 1434.65275 Appl. Anal. 99, No. 4, 569-584 (2020). MSC: 65N30 65N15 35J25 65N12 PDFBibTeX XMLCite \textit{T. Sorokina} and \textit{S. Zhang}, Appl. Anal. 99, No. 4, 569--584 (2020; Zbl 1434.65275) Full Text: DOI
Cui, Ming; Zhang, Shangyou On the uniform convergence of the weak Galerkin finite element method for a singularly-perturbed biharmonic equation. (English) Zbl 1434.65247 J. Sci. Comput. 82, No. 1, Paper No. 5, 15 p. (2020). MSC: 65N30 65N12 31A30 35B25 PDFBibTeX XMLCite \textit{M. Cui} and \textit{S. Zhang}, J. Sci. Comput. 82, No. 1, Paper No. 5, 15 p. (2020; Zbl 1434.65247) Full Text: DOI
Ye, Xiu; Zhang, Shangyou; Zhang, Zhimin A new \(P_1\) weak Galerkin method for the biharmonic equation. (English) Zbl 1427.65342 J. Comput. Appl. Math. 364, Article ID 112337, 10 p. (2020). MSC: 65N15 65N30 35B45 35J50 35J35 PDFBibTeX XMLCite \textit{X. Ye} et al., J. Comput. Appl. Math. 364, Article ID 112337, 10 p. (2020; Zbl 1427.65342) Full Text: DOI
Hu, Jun; Zhang, Shangyou A cubic \(H^3\)-nonconforming finite element. (English) Zbl 1449.65315 Commun. Appl. Math. Comput. 1, No. 1, 81-100 (2019). MSC: 65N30 65N12 PDFBibTeX XMLCite \textit{J. Hu} and \textit{S. Zhang}, Commun. Appl. Math. Comput. 1, No. 1, 81--100 (2019; Zbl 1449.65315) Full Text: DOI
Fan, Ronghong; Liu, Yanru; Zhang, Shuo Mixed schemes for fourth-order DIV equations. (English) Zbl 1421.76154 Comput. Methods Appl. Math. 19, No. 2, 341-357 (2019). MSC: 76M10 65N30 35Q60 76E25 76W05 PDFBibTeX XMLCite \textit{R. Fan} et al., Comput. Methods Appl. Math. 19, No. 2, 341--357 (2019; Zbl 1421.76154) Full Text: DOI
Hong, Qingguo; Wang, Fei; Wu, Shuonan; Xu, Jinchao A unified study of continuous and discontinuous Galerkin methods. (English) Zbl 1412.65214 Sci. China, Math. 62, No. 1, 1-32 (2019). MSC: 65N30 65N12 65N15 35J15 35J30 PDFBibTeX XMLCite \textit{Q. Hong} et al., Sci. China, Math. 62, No. 1, 1--32 (2019; Zbl 1412.65214) Full Text: DOI arXiv
Wu, Shuonan; Xu, Jinchao Nonconforming finite element spaces for \(2m\)th order partial differential equations on \(\mathbb {R}^n\) simplicial grids when \(m=n+1\). (English) Zbl 1407.65304 Math. Comput. 88, No. 316, 531-551 (2019). Reviewer: Abdallah Bradji (Annaba) MSC: 65N30 65N12 65N15 35B25 35J30 PDFBibTeX XMLCite \textit{S. Wu} and \textit{J. Xu}, Math. Comput. 88, No. 316, 531--551 (2019; Zbl 1407.65304) Full Text: DOI arXiv
Wang, Wenqing; Huang, Xuehai; Tang, Kai; Zhou, Ruiyue Morley-Wang-Xu element methods with penalty for a fourth order elliptic singular perturbation problem. (English) Zbl 1397.65296 Adv. Comput. Math. 44, No. 4, 1041-1061 (2018). MSC: 65N30 65N15 35J40 35J35 35B25 PDFBibTeX XMLCite \textit{W. Wang} et al., Adv. Comput. Math. 44, No. 4, 1041--1061 (2018; Zbl 1397.65296) Full Text: DOI arXiv
Chen, Long; Hu, Jun; Huang, Xuehai Multigrid methods for Hellan-Herrmann-Johnson mixed method of Kirchhoff plate bending problems. (English) Zbl 1404.65300 J. Sci. Comput. 76, No. 2, 673-696 (2018). MSC: 65N55 35Q74 74K20 65N12 65N30 PDFBibTeX XMLCite \textit{L. Chen} et al., J. Sci. Comput. 76, No. 2, 673--696 (2018; Zbl 1404.65300) Full Text: DOI arXiv
Zhang, Shuo Regular decomposition and a framework of order reduced methods for fourth order problems. (English) Zbl 1383.35074 Numer. Math. 138, No. 1, 241-271 (2018). MSC: 35J35 65N30 PDFBibTeX XMLCite \textit{S. Zhang}, Numer. Math. 138, No. 1, 241--271 (2018; Zbl 1383.35074) Full Text: DOI arXiv
Gallistl, Dietmar Stable splitting of polyharmonic operators by generalized Stokes systems. (English) Zbl 1369.31012 Math. Comput. 86, No. 308, 2555-2577 (2017). MSC: 31B30 31B35 35J30 65N30 PDFBibTeX XMLCite \textit{D. Gallistl}, Math. Comput. 86, No. 308, 2555--2577 (2017; Zbl 1369.31012) Full Text: DOI Link
Yang, Yidu; Li, Hao; Bi, Hai The lower bound property of the Morley element eigenvalues. (English) Zbl 1359.65244 Comput. Math. Appl. 72, No. 4, 904-920 (2016). MSC: 65N25 35J40 65N50 PDFBibTeX XMLCite \textit{Y. Yang} et al., Comput. Math. Appl. 72, No. 4, 904--920 (2016; Zbl 1359.65244) Full Text: DOI arXiv
Schedensack, M. A new discretization for \(m\)th-Laplace equations with arbitrary polynomial degrees. (English) Zbl 1344.31003 SIAM J. Numer. Anal. 54, No. 4, 2138-2162 (2016). MSC: 31A30 31A35 35J30 65N30 65N12 74K20 PDFBibTeX XMLCite \textit{M. Schedensack}, SIAM J. Numer. Anal. 54, No. 4, 2138--2162 (2016; Zbl 1344.31003) Full Text: DOI arXiv
Hu, Jun; Huang, Yunqing; Ma, Rui Guaranteed lower bounds for eigenvalues of elliptic operators. (English) Zbl 1343.65131 J. Sci. Comput. 67, No. 3, 1181-1197 (2016). Reviewer: Abdallah Bradji (Annaba) MSC: 65N25 65N30 65N15 35J25 35P15 PDFBibTeX XMLCite \textit{J. Hu} et al., J. Sci. Comput. 67, No. 3, 1181--1197 (2016; Zbl 1343.65131) Full Text: DOI
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 PDFBibTeX XMLCite \textit{S. Zhang}, Numer. Math. 133, No. 2, 371--408 (2016; Zbl 1381.76208) Full Text: DOI arXiv
Hu, Jun; Yang, Xueqin Lower bounds of eigenvalues of the biharmonic operators by the rectangular Morley element methods. (English) Zbl 1344.65108 Numer. Methods Partial Differ. Equations 31, No. 5, 1623-1644 (2015). Reviewer: Mahmoud Annaby (Giza) MSC: 65N25 35P15 65N30 35J40 PDFBibTeX XMLCite \textit{J. Hu} and \textit{X. Yang}, Numer. Methods Partial Differ. Equations 31, No. 5, 1623--1644 (2015; Zbl 1344.65108) Full Text: DOI arXiv
Hu, Jun; Zhang, Shangyou The minimal conforming \(H^{k}\) finite element spaces on \(\mathbb R^{n}\) rectangular grids. (English) Zbl 1307.65167 Math. Comput. 84, No. 292, 563-579 (2015). MSC: 65N30 65N50 PDFBibTeX XMLCite \textit{J. Hu} and \textit{S. Zhang}, Math. Comput. 84, No. 292, 563--579 (2015; Zbl 1307.65167) Full Text: DOI
Hu, Jun; Huang, Yunqing; Lin, Qun Lower bounds for eigenvalues of elliptic operators: by nonconforming finite element methods. (English) Zbl 1335.65089 J. Sci. Comput. 61, No. 1, 196-221 (2014). MSC: 65N25 65N30 35J25 35P15 65N15 PDFBibTeX XMLCite \textit{J. Hu} et al., J. Sci. Comput. 61, No. 1, 196--221 (2014; Zbl 1335.65089) Full Text: DOI arXiv