Carstensen, Carsten; Gräßle, Benedikt; Nataraj, Neela Unifying a posteriori error analysis of five piecewise quadratic discretisations for the biharmonic equation. (English) Zbl 07818545 J. Numer. Math. 32, No. 1, 77-109 (2024). MSC: 65N30 65N12 65N15 65N50 31A30 PDFBibTeX XMLCite \textit{C. Carstensen} et al., J. Numer. Math. 32, No. 1, 77--109 (2024; Zbl 07818545) Full Text: DOI arXiv
Carstensen, Carsten; Khot, Rekha; Pani, Amiya K. Nonconforming virtual elements for the biharmonic equation with Morley degrees of freedom on polygonal meshes. (English) Zbl 1528.65103 SIAM J. Numer. Anal. 61, No. 5, 2460-2484 (2023). Reviewer: Xiaodi Zhang (Zhengzhou) MSC: 65N30 65N50 65N12 65N15 31A30 PDFBibTeX XMLCite \textit{C. Carstensen} et al., SIAM J. Numer. Anal. 61, No. 5, 2460--2484 (2023; Zbl 1528.65103) Full Text: DOI arXiv
Dong, Z.; Mascotto, L. \(hp\)-optimal interior penalty discontinuous Galerkin methods for the biharmonic problem. (English) Zbl 07708372 J. Sci. Comput. 96, No. 1, Paper No. 30, 32 p. (2023). MSC: 65N30 65N50 65N12 65N15 31A30 76D07 35Q35 PDFBibTeX XMLCite \textit{Z. Dong} and \textit{L. Mascotto}, J. Sci. Comput. 96, No. 1, Paper No. 30, 32 p. (2023; Zbl 07708372) Full Text: DOI arXiv
Carstensen, Carsten; Puttkammer, Sophie Direct guaranteed lower eigenvalue bounds with optimal a priori convergence rates for the bi-Laplacian. (English) Zbl 1521.65118 SIAM J. Numer. Anal. 61, No. 2, 812-836 (2023). Reviewer: Chandrasekhar Salimath (Bengaluru) MSC: 65N25 65N30 65N15 65N12 65D05 65N50 49J35 31A30 PDFBibTeX XMLCite \textit{C. Carstensen} and \textit{S. Puttkammer}, SIAM J. Numer. Anal. 61, No. 2, 812--836 (2023; Zbl 1521.65118) Full Text: DOI arXiv
Xu, Minqiang; Shi, Chungang A Hessian recovery-based finite difference method for biharmonic problems. (English) Zbl 1524.65870 Appl. Math. Lett. 137, Article ID 108503, 7 p. (2023). MSC: 65N30 65N12 65N50 65N15 35J40 31A30 PDFBibTeX XMLCite \textit{M. Xu} and \textit{C. Shi}, Appl. Math. Lett. 137, Article ID 108503, 7 p. (2023; Zbl 1524.65870) Full Text: DOI
Anderson, Jude T.; Williams, David M. Space-time hypervolume meshing part 1: Point insertion, geometric predicates, and bistellar flips. arXiv:2312.17414 Preprint, arXiv:2312.17414 [math.NA] (2023). MSC: 65M50 52B11 31B99 76M10 BibTeX Cite \textit{J. T. Anderson} and \textit{D. M. Williams}, ``Space-time hypervolume meshing part 1: Point insertion, geometric predicates, and bistellar flips'', Preprint, arXiv:2312.17414 [math.NA] (2023) Full Text: arXiv OA License
Anderson, Jude T.; Williams, David M.; Corrigan, Andrew Surface and hypersurface meshing techniques for space-time finite element methods. arXiv:2301.12079 Preprint, arXiv:2301.12079 [math.NA] (2023). MSC: 65M50 52B11 31B99 76M10 BibTeX Cite \textit{J. T. Anderson} et al., ``Surface and hypersurface meshing techniques for space-time finite element methods'', Preprint, arXiv:2301.12079 [math.NA] (2023) Full Text: arXiv OA License
Shapeev, Vasiliĭ Pavlovich; Bryndin, Luka Sergeevich; Belyaev, Vasiliĭ Alekseevich The \(hp\)-version of the least-squares collocation method with integral collocation for solving a biharmonic equation. (Russian. English summary) Zbl 1513.65487 Vestn. Samar. Gos. Tekh. Univ., Ser. Fiz.-Mat. Nauki 26, No. 3, 556-572 (2022). MSC: 65N35 65K10 65M50 65F08 65F10 65F20 65M12 31A30 35J48 74K10 PDFBibTeX XMLCite \textit{V. P. Shapeev} et al., Vestn. Samar. Gos. Tekh. Univ., Ser. Fiz.-Mat. Nauki 26, No. 3, 556--572 (2022; Zbl 1513.65487) Full Text: DOI MNR
Burman, Erik; Hansbo, Peter; Larson, Mats G. CutFEM based on extended finite element spaces. (English) Zbl 1497.65221 Numer. Math. 152, No. 2, 331-369 (2022). MSC: 65N30 65N85 65N50 65N12 35B35 35B65 35B45 31A30 PDFBibTeX XMLCite \textit{E. Burman} et al., Numer. Math. 152, No. 2, 331--369 (2022; Zbl 1497.65221) Full Text: DOI arXiv
Ye, Xiu; Zhang, Shangyou A \(C^0\)-conforming DG finite element method for biharmonic equations on triangle/tetrahedron. (English) Zbl 1517.65121 J. Numer. Math. 30, No. 3, 163-172 (2022). MSC: 65N30 65N50 65N15 65N12 31A30 PDFBibTeX XMLCite \textit{X. Ye} and \textit{S. Zhang}, J. Numer. Math. 30, No. 3, 163--172 (2022; Zbl 1517.65121) Full Text: DOI
Mallik, Gouranga Goal-oriented a posteriori error estimation for the biharmonic problem based on an equilibrated moment tensor. (English) Zbl 1524.65845 Comput. Math. Appl. 117, 312-325 (2022). MSC: 65N30 65N15 65N50 35J25 74S05 31A30 74K20 35Q74 PDFBibTeX XMLCite \textit{G. Mallik}, Comput. Math. Appl. 117, 312--325 (2022; Zbl 1524.65845) Full Text: DOI arXiv
Zhao, Lina; Park, Eun-Jae; Kim, Wonjong A staggered cell-centered DG method for the biharmonic Steklov problem on polygonal meshes: a priori and a posteriori analysis. (English) Zbl 1524.65883 Comput. Math. Appl. 117, 216-228 (2022). MSC: 65N30 65N15 65N12 35J40 74K20 31A30 65N85 65N50 35Q74 PDFBibTeX XMLCite \textit{L. Zhao} et al., Comput. Math. Appl. 117, 216--228 (2022; Zbl 1524.65883) Full Text: DOI
Ye, Xiu; Zhang, Shangyou A weak divergence CDG method for the biharmonic equation on triangular and tetrahedral meshes. (English) Zbl 1493.65237 Appl. Numer. Math. 178, 155-165 (2022). MSC: 65N30 65N50 65N15 35J05 31A30 PDFBibTeX XMLCite \textit{X. Ye} and \textit{S. Zhang}, Appl. Numer. Math. 178, 155--165 (2022; Zbl 1493.65237) Full Text: DOI
Carstensen, Carsten; Nataraj, Neela Lowest-order equivalent nonstandard finite element methods for biharmonic plates. (English) Zbl 1483.65177 ESAIM, Math. Model. Numer. Anal. 56, No. 1, 41-78 (2022). MSC: 65N30 65N12 65N15 65N50 31A30 74K20 PDFBibTeX XMLCite \textit{C. Carstensen} and \textit{N. Nataraj}, ESAIM, Math. Model. Numer. Anal. 56, No. 1, 41--78 (2022; Zbl 1483.65177) Full Text: DOI arXiv
Guan, Qingguang Some estimates of virtual element methods for fourth order problems. (English) Zbl 1478.65126 Electron. Res. Arch. 29, No. 6, 4099-4118 (2021). MSC: 65N30 65N50 35J40 65N15 31A30 PDFBibTeX XMLCite \textit{Q. Guan}, Electron. Res. Arch. 29, No. 6, 4099--4118 (2021; Zbl 1478.65126) Full Text: DOI arXiv
Zhang, Shangyou Erratum to: “A C1-P2 finite element without nodal basis”. (English) Zbl 1479.65032 ESAIM, Math. Model. Numer. Anal. 55, Suppl., 877-878 (2021). Reviewer: Dana Černá (Liberec) MSC: 65N30 65N12 35J40 65N50 31A30 PDFBibTeX XMLCite \textit{S. Zhang}, ESAIM, Math. Model. Numer. Anal. 55, 877--878 (2021; Zbl 1479.65032) Full Text: DOI
Dong, Zhaonan; Mascotto, Lorenzo; Sutton, Oliver J. Residual-based a posteriori error estimates for \(hp\)-discontinuous Galerkin discretizations of the biharmonic problem. (English) Zbl 1473.65297 SIAM J. Numer. Anal. 59, No. 3, 1273-1298 (2021). MSC: 65N30 65N12 65N15 65N50 31A30 PDFBibTeX XMLCite \textit{Z. Dong} et al., SIAM J. Numer. Anal. 59, No. 3, 1273--1298 (2021; Zbl 1473.65297) Full Text: DOI arXiv
Huang, Yunqing; Wei, Huayi; Yang, Wei; Yi, Nianyu Recovery based finite element method for biharmonic equation in 2D. (English) Zbl 1463.65373 J. Comput. Math. 38, No. 1, 84-102 (2020). MSC: 65N30 31A30 65N50 PDFBibTeX XMLCite \textit{Y. Huang} et al., J. Comput. Math. 38, No. 1, 84--102 (2020; Zbl 1463.65373) Full Text: DOI arXiv
Li, Hao; Bi, Hai; Yang, Yidu The two-grid and multigrid discretizations of the \(C^0\)IPG method for biharmonic eigenvalue problem. (English) Zbl 1437.65173 Discrete Contin. Dyn. Syst., Ser. B 25, No. 5, 1775-1789 (2020). MSC: 65N25 65N30 65N55 65N50 65F15 31A30 PDFBibTeX XMLCite \textit{H. Li} et al., Discrete Contin. Dyn. Syst., Ser. B 25, No. 5, 1775--1789 (2020; Zbl 1437.65173) Full Text: DOI
Chen, Yanping; Lin, Xiuxiu; Huang, Yunqing; Lin, Qian \(hp\) spectral element approximation for integral state constrained optimal control problems governed by harmonic equations. (English) Zbl 1440.65244 J. Comput. Appl. Math. 371, Article ID 112716, 13 p. (2020). MSC: 65N35 65N15 65N50 31A30 49K20 93C20 35Q93 35B45 PDFBibTeX XMLCite \textit{Y. Chen} et al., J. Comput. Appl. Math. 371, Article ID 112716, 13 p. (2020; Zbl 1440.65244) Full Text: DOI
Dong, Zhaonan Discontinuous Galerkin methods for the biharmonic problem on polygonal and polyhedral meshes. (English) Zbl 1434.65249 Int. J. Numer. Anal. Model. 16, No. 5, 825-846 (2019). MSC: 65N30 65N50 65N15 31A30 PDFBibTeX XMLCite \textit{Z. Dong}, Int. J. Numer. Anal. Model. 16, No. 5, 825--846 (2019; Zbl 1434.65249) Full Text: arXiv Link
Banz, Lothar; Petsche, Jan; Schröder, Andreas Two stabilized three-field formulations for the biharmonic problem. (English) Zbl 1433.65275 Apel, Thomas (ed.) et al., Advanced finite element methods with applications. Selected papers from the 30th Chemnitz finite element symposium, St. Wolfgang/Strobl, Austria, September 25–27, 2017. Cham: Springer. Lect. Notes Comput. Sci. Eng. 128, 41-55 (2019). MSC: 65N30 65N12 65N15 65N50 35J30 31A30 35B45 PDFBibTeX XMLCite \textit{L. Banz} et al., Lect. Notes Comput. Sci. Eng. 128, 41--55 (2019; Zbl 1433.65275) Full Text: DOI
Braess, Dietrich; Hoppe, R. H. W.; Linsenmann, Christopher A two-energies principle for the biharmonic equation and an a posteriori error estimator for an interior penalty discontinous Galerkin approximation. (English) Zbl 1419.31004 ESAIM, Math. Model. Numer. Anal. 52, No. 6, 2479-2504 (2018). MSC: 31A30 65N30 65N50 PDFBibTeX XMLCite \textit{D. Braess} et al., ESAIM, Math. Model. Numer. Anal. 52, No. 6, 2479--2504 (2018; Zbl 1419.31004) Full Text: DOI
Kato, Hatsuhiro; Kato, Hatsuyoshi; Naito, Yoshimasa Mechanics shape function of quadrilateral element composed of subdivision triangles for recursive transfer method. (English) Zbl 1450.65104 Japan J. Ind. Appl. Math. 35, No. 1, 277-295 (2018). Reviewer: Abdallah Bradji (Annaba) MSC: 65M22 65M50 74K20 74J20 31A30 PDFBibTeX XMLCite \textit{H. Kato} et al., Japan J. Ind. Appl. Math. 35, No. 1, 277--295 (2018; Zbl 1450.65104) Full Text: DOI
Bondarenko, A. V.; Hardin, D. P.; Saff, E. B. Mesh ratios for best-packing and limits of minimal energy configurations. (English) Zbl 1349.31004 Acta Math. Hung. 142, No. 1, 118-131 (2014). MSC: 31C20 65N50 57N16 52A40 28A78 PDFBibTeX XMLCite \textit{A. V. Bondarenko} et al., Acta Math. Hung. 142, No. 1, 118--131 (2014; Zbl 1349.31004) Full Text: DOI arXiv Link
Guadie, Maru; Malinnikova, Eugenia Stability and regularization for determining sets of discrete Laplacian. (English) Zbl 1282.65139 Inverse Probl. 29, No. 7, Article ID 075018, 17 p. (2013). Reviewer: Vladimir L. Makarov (Kyïv) MSC: 65N21 31A05 31A25 65N50 65E05 65N15 35R30 PDFBibTeX XMLCite \textit{M. Guadie} and \textit{E. Malinnikova}, Inverse Probl. 29, No. 7, Article ID 075018, 17 p. (2013; Zbl 1282.65139) Full Text: DOI
Wang, Tongke A mixed finite volume element method based on rectangular mesh for biharmonic equations. (English) Zbl 1057.65088 J. Comput. Appl. Math. 172, No. 1, 117-130 (2004). Reviewer: Gerald W. Hedstrom (Pleasanton) MSC: 65N30 35J40 31A30 65N15 65N50 PDFBibTeX XMLCite \textit{T. Wang}, J. Comput. Appl. Math. 172, No. 1, 117--130 (2004; Zbl 1057.65088) Full Text: DOI
Zhang, Jianming; Tanaka, Masataka; Matsumoto, Toshiro Meshless analysis of potential problems in three dimensions with the hybrid boundary node method. (English) Zbl 1048.65121 Int. J. Numer. Methods Eng. 59, No. 9, 1147-1166 (2004). MSC: 65N38 65N12 65N50 31B10 31B20 35J05 PDFBibTeX XMLCite \textit{J. Zhang} et al., Int. J. Numer. Methods Eng. 59, No. 9, 1147--1166 (2004; Zbl 1048.65121) Full Text: DOI
Shi, Zhongci; Xie, Zhenghui Multigrid methods for Morley element on nonnested meshes. (English) Zbl 0916.65112 J. Comput. Math. 16, No. 5, 385-394 (1998). Reviewer: Michael Sever (Jerusalem) MSC: 65N55 74S05 35J40 31A30 74K20 65N30 65N50 65F10 65F35 PDFBibTeX XMLCite \textit{Z. Shi} and \textit{Z. Xie}, J. Comput. Math. 16, No. 5, 385--394 (1998; Zbl 0916.65112)
Verfürth, Rüdiger A review of a posteriori error estimation and adaptive mesh-refinement techniques. (English) Zbl 0853.65108 Wiley-Teubner Series Advances in Numerical Mathematics. Chichester: John Wiley & Sons. Stuttgart: B. G. Teubner. vi, 127 p. (1996). Reviewer: P.Matus (Minsk) MSC: 65N15 65N30 65N50 35Q30 35J05 35J65 31A30 PDFBibTeX XMLCite \textit{R. Verfürth}, A review of a posteriori error estimation and adaptive mesh-refinement techniques. Chichester: John Wiley \& Sons; Stuttgart: B. G. Teubner (1996; Zbl 0853.65108)
Kita, E.; Kamiya, N. Sample point error estimation for plane quasi-harmonic equations. (English) Zbl 0840.65118 Brebbia, C. A. (ed.) et al., Boundary elements XVII. Proceedings of the 17th international conference on boundary elements, BEM 17, held in Madison, WI, USA, in July 1995. Southampton: Computational Mechanics Publications. Boundary Elem. 17, 107-114 (1995). MSC: 65N38 74S15 65N15 65N50 31A10 35J40 PDFBibTeX XMLCite \textit{E. Kita} and \textit{N. Kamiya}, in: Boundary elements XVII. Proceedings of the 17th international conference on boundary elements, BEM 17, held in Madison, WI, USA, in July 1995. Southampton: Computational Mechanics Publications. 107--114 (1995; Zbl 0840.65118)
Dong, Y. F.; Parreira, P. \(h\)-adaptive BEM based on linear hierarchical functions. (English) Zbl 0827.65110 Brebbia, C. A. (ed.) et al., Boundary elements XIV. Vol. 1: Field problems and applications. Proceedings of the 14th international conference on boundary element methods, BEM 14, held in Sevilla, Spain, 1992. Southampton: Computational Mechanics Publications. 653-665 (1992). MSC: 65N38 65N12 65N50 31A30 35J05 PDFBibTeX XMLCite \textit{Y. F. Dong} and \textit{P. Parreira}, in: Boundary elements XIV. Vol. 1: Field problems and applications. Proceedings of the 14th international conference on boundary element methods, BEM 14, held in Sevilla, Spain, 1992. Southampton: Computational Mechanics Publications; London: Elsevier Science Publishers. 653--665 (1992; Zbl 0827.65110)
Zamani, N. G.; Sun, W. Adaptive \(r\) and \(h-r\) algorithms for boundary elements. (English) Zbl 0770.65077 Adv. Eng. Softw. 15, No. 3-4, 241-247 (1992). Reviewer: J.Vaníček (Praha) MSC: 65N38 65N50 35J40 31A30 74B05 PDFBibTeX XMLCite \textit{N. G. Zamani} and \textit{W. Sun}, Adv. Eng. Softw. 15, No. 3--4, 241--247 (1992; Zbl 0770.65077) Full Text: DOI
Sparis, Panagiotis D.; Karkanis, Anastasios Boundary-orthogonal biharmonic grids via preconditioned gradient methods. (English) Zbl 0766.76063 AIAA J. 30, No. 3, 671-678 (1992). MSC: 76M20 65M50 90C52 31A30 PDFBibTeX XMLCite \textit{P. D. Sparis} and \textit{A. Karkanis}, AIAA J. 30, No. 3, 671--678 (1992; Zbl 0766.76063) Full Text: DOI
Sparis, Panagiotis D.; Karkanis, Anastasios; Pergantis, Stelianos Conjugate method solutions of the biharmonic equation for the generation of boundary orthogonal grids. (English) Zbl 0814.65112 Comput. Methods Appl. Mech. Eng. 98, No. 2, 273-290 (1992). MSC: 65N50 65N06 65F10 35J40 31A30 PDFBibTeX XMLCite \textit{P. D. Sparis} et al., Comput. Methods Appl. Mech. Eng. 98, No. 2, 273--290 (1992; Zbl 0814.65112) Full Text: DOI
Abou El-Seoud, M. S. An adaptive multi-grid algorithm for the numerical solution of quasilinear potential equations. (English) Zbl 0572.65090 Computing 35, 307-324 (1985). MSC: 65N22 65N15 35J65 31A25 53A10 65E05 65H10 65N50 PDFBibTeX XMLCite \textit{M. S. Abou El-Seoud}, Computing 35, 307--324 (1985; Zbl 0572.65090) Full Text: DOI
Linden, Johannes A multigrid method for solving the biharmonic equation on rectangular domains. (English) Zbl 0568.65067 Arbeitspapiere der GMD 143. St. Augustin: GMD. 13 p. (1985). Reviewer: J.Mandel MSC: 65N22 65N50 31A30 35J05 35J40 PDFBibTeX XMLCite \textit{J. Linden}, A multigrid method for solving the biharmonic equation on rectangular domains. St. Augustin: GMD (1985; Zbl 0568.65067)
Blum, H. Zur Gitterverfeinerung für quasilineare Probleme auf Eckengebieten. (German) Zbl 0576.65107 Z. Angew. Math. Mech. 64, No. 5, T264-T266 (1984). MSC: 65N30 65N50 31A30 35J65 PDFBibTeX XMLCite \textit{H. Blum}, Z. Angew. Math. Mech. 64, T264--T266 (1984; Zbl 0576.65107)
Laasonen, P. Über die lokale Verkleinerung der Maschen und die Konvergenz des Netzverfahrens. (German) Zbl 0523.65082 Z. Angew. Math. Mech. 63, 68-70 (1983). MSC: 65N50 65N12 35J05 31A25 PDFBibTeX XMLCite \textit{P. Laasonen}, Z. Angew. Math. Mech. 63, 68--70 (1983; Zbl 0523.65082) Full Text: DOI
Shubin, G. R.; Stephens, A. B.; Bell, J. B. Three dimensional grid generation using biharmonics. (English) Zbl 0504.65067 Appl. Math. Comput. 10-11, 761-774 (1982). MSC: 65N50 65N06 31B30 35J40 65N22 65F10 PDFBibTeX XMLCite \textit{G. R. Shubin} et al., Appl. Math. Comput. 10--11, 761--774 (1982; Zbl 0504.65067) Full Text: DOI