Meng, Jian; Mei, Liquan; Fei, Mingfa \( \boldsymbol{H}^1\)-conforming virtual element method for the Laplacian eigenvalue problem in mixed form. (English) Zbl 1519.65050 J. Comput. Appl. Math. 436, Article ID 115395, 17 p. (2024). MSC: 65N25 65N30 65N15 PDFBibTeX XMLCite \textit{J. Meng} et al., J. Comput. Appl. Math. 436, Article ID 115395, 17 p. (2024; Zbl 1519.65050) Full Text: DOI
Inzunza, Daniel; Lepe, Felipe; Rivera, Gonzalo Displacement-pseudostress formulation for the linear elasticity spectral problem. (English) Zbl 07776995 Numer. Methods Partial Differ. Equations 39, No. 3, 1996-2017 (2023). MSC: 65-XX 35-XX PDFBibTeX XMLCite \textit{D. Inzunza} et al., Numer. Methods Partial Differ. Equations 39, No. 3, 1996--2017 (2023; Zbl 07776995) Full Text: DOI arXiv
Liu, Xuefeng; Vejchodský, Tomáš Projection-based guaranteed \(L^2\) error bounds for finite element approximations of Laplace eigenfunctions. (English) Zbl 1518.65125 J. Comput. Appl. Math. 429, Article ID 115164, 12 p. (2023). MSC: 65N25 65N30 65N15 PDFBibTeX XMLCite \textit{X. Liu} and \textit{T. Vejchodský}, J. Comput. Appl. Math. 429, Article ID 115164, 12 p. (2023; Zbl 1518.65125) Full Text: DOI arXiv
Lederer, Philip L. Asymptotically exact a posteriori error estimates for the BDM finite element approximation of mixed Laplace eigenvalue problems. (English) Zbl 07692056 BIT 63, No. 2, Paper No. 34, 21 p. (2023). MSC: 65N25 65N30 65N15 PDFBibTeX XMLCite \textit{P. L. Lederer}, BIT 63, No. 2, Paper No. 34, 21 p. (2023; Zbl 07692056) Full Text: DOI arXiv
Lepe, F.; Mora, D.; Rivera, G.; Velásquez, I. A posteriori virtual element method for the acoustic vibration problem. (English) Zbl 1511.65125 Adv. Comput. Math. 49, No. 1, Paper No. 10, 29 p. (2023). MSC: 65N30 65N25 65N15 65N12 76Q05 74F10 74H45 76M10 74S05 PDFBibTeX XMLCite \textit{F. Lepe} et al., Adv. Comput. Math. 49, No. 1, Paper No. 10, 29 p. (2023; Zbl 1511.65125) Full Text: DOI arXiv
Lepe, Felipe; Rivera, Gonzalo; Vellojin, Jesus Error estimates for a vorticity-based velocity-stress formulation of the Stokes eigenvalue problem. (English) Zbl 1497.65214 J. Comput. Appl. Math. 420, Article ID 114798, 20 p. (2023). MSC: 65N25 35Q35 65N15 65N30 65N50 76D07 PDFBibTeX XMLCite \textit{F. Lepe} et al., J. Comput. Appl. Math. 420, Article ID 114798, 20 p. (2023; Zbl 1497.65214) Full Text: DOI arXiv
Lepe, Felipe; Rivera, Gonzalo; Vellojin, Jesus A posteriori analysis for a mixed FEM discretization of the linear elasticity spectral problem. (English) Zbl 1512.65272 J. Sci. Comput. 93, No. 1, Paper No. 10, 25 p. (2022). MSC: 65N30 65N25 65N15 65N50 35M10 35A15 35J15 74B05 74S05 35Q74 PDFBibTeX XMLCite \textit{F. Lepe} et al., J. Sci. Comput. 93, No. 1, Paper No. 10, 25 p. (2022; Zbl 1512.65272) Full Text: DOI arXiv
Liu, Xuefeng; Vejchodský, Tomáš Fully computable a posteriori error bounds for eigenfunctions. (English) Zbl 1496.65204 Numer. Math. 152, No. 1, 183-221 (2022). MSC: 65N25 65N30 65N15 65F15 PDFBibTeX XMLCite \textit{X. Liu} and \textit{T. Vejchodský}, Numer. Math. 152, No. 1, 183--221 (2022; Zbl 1496.65204) Full Text: DOI arXiv
Lepe, Felipe; Rivera, Gonzalo; Vellojin, Jesus Mixed methods for the velocity-pressure-pseudostress formulation of the Stokes eigenvalue problem. (English) Zbl 1491.35340 SIAM J. Sci. Comput. 44, No. 3, A1358-A1380 (2022). MSC: 35Q35 76D07 65N30 65N25 65N15 65N12 65N50 PDFBibTeX XMLCite \textit{F. Lepe} et al., SIAM J. Sci. Comput. 44, No. 3, A1358--A1380 (2022; Zbl 1491.35340) Full Text: DOI arXiv
Querales, J.; Venegas, P. Mixed approximation of the axisymmetric acoustic eigenvalue problem. (English) Zbl 1524.65742 Comput. Math. Appl. 108, 1-11 (2022). MSC: 65N25 65N30 65N15 76M10 74F10 65N12 76Q05 PDFBibTeX XMLCite \textit{J. Querales} and \textit{P. Venegas}, Comput. Math. Appl. 108, 1--11 (2022; Zbl 1524.65742) Full Text: DOI
Bertrand, Fleurianne; Boffi, Daniele; Ma, Rui An adaptive finite element scheme for the Hellinger-Reissner elasticity mixed eigenvalue problem. (English) Zbl 1473.65278 Comput. Methods Appl. Math. 21, No. 3, 501-512 (2021). MSC: 65N25 65N30 65N50 74B05 PDFBibTeX XMLCite \textit{F. Bertrand} et al., Comput. Methods Appl. Math. 21, No. 3, 501--512 (2021; Zbl 1473.65278) Full Text: DOI arXiv
Bertrand, Fleurianne; Boffi, Daniele; Stenberg, Rolf Asymptotically exact a posteriori error analysis for the mixed Laplace eigenvalue problem. (English) Zbl 1436.65166 Comput. Methods Appl. Math. 20, No. 2, 215-225 (2020). MSC: 65N25 65N30 65N15 PDFBibTeX XMLCite \textit{F. Bertrand} et al., Comput. Methods Appl. Math. 20, No. 2, 215--225 (2020; Zbl 1436.65166) Full Text: DOI arXiv
Boffi, Daniele; Gastaldi, Lucia; Rodríguez, Rodolfo; Šebestová, Ivana A posteriori error estimates for Maxwell’s eigenvalue problem. (English) Zbl 1417.78005 J. Sci. Comput. 78, No. 2, 1250-1271 (2019). MSC: 78M10 65N30 65N25 65N15 PDFBibTeX XMLCite \textit{D. Boffi} et al., J. Sci. Comput. 78, No. 2, 1250--1271 (2019; Zbl 1417.78005) Full Text: DOI
Calo, Victor; Cicuttin, Matteo; Deng, Quanling; Ern, Alexandre Spectral approximation of elliptic operators by the hybrid high-order method. (English) Zbl 1422.65359 Math. Comput. 88, No. 318, 1559-1586 (2019). Reviewer: Pavel Burda (Praha) MSC: 65N25 65N30 35J25 65N15 35P15 PDFBibTeX XMLCite \textit{V. Calo} et al., Math. Comput. 88, No. 318, 1559--1586 (2019; Zbl 1422.65359) Full Text: DOI arXiv
Boffi, Daniele; Gastaldi, Lucia Adaptive finite element method for the Maxwell eigenvalue problem. (English) Zbl 1412.65202 SIAM J. Numer. Anal. 57, No. 1, 478-494 (2019). MSC: 65N30 65N25 35Q61 65N50 78M10 PDFBibTeX XMLCite \textit{D. Boffi} and \textit{L. Gastaldi}, SIAM J. Numer. Anal. 57, No. 1, 478--494 (2019; Zbl 1412.65202) Full Text: DOI arXiv
Kim, Kwang-Yeon Postprocessing for the Raviart-Thomas mixed finite element approximation of the eigenvalue problem. (English) Zbl 1427.65346 Korean J. Math. 26, No. 3, 467-481 (2018). MSC: 65N25 65N30 35P15 PDFBibTeX XMLCite \textit{K.-Y. Kim}, Korean J. Math. 26, No. 3, 467--481 (2018; Zbl 1427.65346) Full Text: DOI
Cancès, Eric; Dusson, Geneviève; Maday, Yvon; Stamm, Benjamin; Vohralík, Martin Guaranteed and robust a posteriori bounds for Laplace eigenvalues and eigenvectors: a unified framework. (English) Zbl 1402.65137 Numer. Math. 140, No. 4, 1033-1079 (2018). MSC: 65N15 35P15 65N25 65N30 65N50 PDFBibTeX XMLCite \textit{E. Cancès} et al., Numer. Math. 140, No. 4, 1033--1079 (2018; Zbl 1402.65137) Full Text: DOI Link
Boffi, Daniele; Gallistl, Dietmar; Gardini, Francesca; Gastaldi, Lucia Optimal convergence of adaptive FEM for eigenvalue clusters in mixed form. (English) Zbl 1364.65234 Math. Comput. 86, No. 307, 2213-2237 (2017). MSC: 65N25 65N30 35P15 65N12 PDFBibTeX XMLCite \textit{D. Boffi} et al., Math. Comput. 86, No. 307, 2213--2237 (2017; Zbl 1364.65234) Full Text: DOI arXiv
He, Wenming; Zhang, Zhimin \(2k\) superconvergence of \(Q_k\) finite elements by anisotropic mesh approximation in weighted Sobolev spaces. (English) Zbl 1361.65085 Math. Comput. 86, No. 306, 1693-1718 (2017). MSC: 65N12 65N15 65N30 35J05 PDFBibTeX XMLCite \textit{W. He} and \textit{Z. Zhang}, Math. Comput. 86, No. 306, 1693--1718 (2017; Zbl 1361.65085) Full Text: DOI
Shi, Dongyang; Wang, Lele; Liao, Xin A new nonconforming mixed finite element scheme for second order eigenvalue problem. (English) Zbl 1410.65438 Appl. Math. Comput. 273, 842-855 (2016). MSC: 65N25 65N30 35J25 35P05 PDFBibTeX XMLCite \textit{D. Shi} et al., Appl. Math. Comput. 273, 842--855 (2016; Zbl 1410.65438) Full Text: DOI
Zeng, Yuping; Chen, Jinru; Wang, Feng A posteriori error estimates of a weakly over-penalized symmetric interior penalty method for elliptic eigenvalue problems. (English) Zbl 1457.65176 East Asian J. Appl. Math. 5, No. 4, 327-341 (2015). MSC: 65N25 65N30 65N15 PDFBibTeX XMLCite \textit{Y. Zeng} et al., East Asian J. Appl. Math. 5, No. 4, 327--341 (2015; Zbl 1457.65176) Full Text: DOI
Hu, Jun; Ma, Rui The enriched Crouzeix-Raviart elements are equivalent to the Raviart-Thomas elements. (English) Zbl 1319.65111 J. Sci. Comput. 63, No. 2, 410-425 (2015). MSC: 65N30 65N15 65N25 35J05 35Q30 35P15 PDFBibTeX XMLCite \textit{J. Hu} and \textit{R. Ma}, J. Sci. Comput. 63, No. 2, 410--425 (2015; Zbl 1319.65111) Full Text: DOI arXiv
Yang, Yidu; Han, Jiayu; Bi, Hai; Yu, Yuanyuan The lower/upper bound property of the Crouzeix-Raviart element eigenvalues on adaptive meshes. (English) Zbl 1320.65163 J. Sci. Comput. 62, No. 1, 284-299 (2015). Reviewer: Adrian Carabineanu (Bucureşti) MSC: 65N25 35P15 65N30 65N50 65N15 PDFBibTeX XMLCite \textit{Y. Yang} et al., J. Sci. Comput. 62, No. 1, 284--299 (2015; Zbl 1320.65163) Full Text: DOI
Yu, Yuanyuan; Yang, Yidu; Han, Jiayu An adaptive nonconforming finite element algorithm for Laplace eigenvalue problem. (English) Zbl 1470.65200 Abstr. Appl. Anal. 2014, Article ID 189490, 15 p. (2014). MSC: 65N30 65N15 65N25 PDFBibTeX XMLCite \textit{Y. Yu} et al., Abstr. Appl. Anal. 2014, Article ID 189490, 15 p. (2014; Zbl 1470.65200) Full Text: DOI
Yang, Yidu; Sun, Lingling; Bi, Hai; Li, Hao A note on the residual type a posteriori error estimates for finite element eigenpairs of nonsymmetric elliptic eigenvalue problems. (English) Zbl 1291.65334 Appl. Numer. Math. 82, 51-67 (2014). MSC: 65N25 65N15 65N30 PDFBibTeX XMLCite \textit{Y. Yang} et al., Appl. Numer. Math. 82, 51--67 (2014; Zbl 1291.65334) Full Text: DOI
Boffi, Daniele; Gastaldi, Lucia Some remarks on finite element approximation of multiple eigenvalues. (English) Zbl 1329.65260 Appl. Numer. Math. 79, 18-28 (2014). MSC: 65N25 65N30 PDFBibTeX XMLCite \textit{D. Boffi} and \textit{L. Gastaldi}, Appl. Numer. Math. 79, 18--28 (2014; Zbl 1329.65260) Full Text: DOI
Yang, YiDu; Jiang, Wei Upper spectral bounds and a posteriori error analysis of several mixed finite element approximations for the Stokes eigenvalue problem. (English) Zbl 1273.65171 Sci. China, Math. 56, No. 6, 1313-1330 (2013). Reviewer: Costică Moroşanu (Iaşi) MSC: 65N25 65N30 PDFBibTeX XMLCite \textit{Y. Yang} and \textit{W. Jiang}, Sci. China, Math. 56, No. 6, 1313--1330 (2013; Zbl 1273.65171) Full Text: DOI
Jia, ShangHui; Chen, HongTao; Xie, HeHu A posteriori error estimator for eigenvalue problems by mixed finite element method. (English) Zbl 1264.65192 Sci. China, Math. 56, No. 5, 887-900 (2013). MSC: 65N30 65N25 65L15 65B99 PDFBibTeX XMLCite \textit{S. Jia} et al., Sci. China, Math. 56, No. 5, 887--900 (2013; Zbl 1264.65192) Full Text: DOI
Cliffe, K. Andrew; Hall, Edward J. C.; Houston, Paul; Phipps, Eric T.; Salinger, Andrew G. Adaptivity and a posteriori error control for bifurcation problems. II: Incompressible fluid flow in open systems with \(Z_{2}\) symmetry. (English) Zbl 1311.76052 J. Sci. Comput. 47, No. 3, 389-418 (2011). MSC: 76M10 65N30 65N15 76D05 PDFBibTeX XMLCite \textit{K. A. Cliffe} et al., J. Sci. Comput. 47, No. 3, 389--418 (2011; Zbl 1311.76052) Full Text: DOI
Chen, Hongtao; Jia, Shanghui; Xie, Hehu Postprocessing and higher order convergence for the mixed finite element approximations of the eigenvalue problem. (English) Zbl 1209.65126 Appl. Numer. Math. 61, No. 4, 615-629 (2011). Reviewer: Calin Ioan Gheorghiu (Cluj-Napoca) MSC: 65N25 65N12 35P15 65N30 PDFBibTeX XMLCite \textit{H. Chen} et al., Appl. Numer. Math. 61, No. 4, 615--629 (2011; Zbl 1209.65126) Full Text: DOI
Armentano, M. G.; Padra, C.; Rodríguez, R.; Scheble, M. An hp finite element adaptive scheme to solve the Laplace model for fluid-solid vibrations. (English) Zbl 1225.74078 Comput. Methods Appl. Mech. Eng. 200, No. 1-4, 178-188 (2011). MSC: 74S05 74F10 PDFBibTeX XMLCite \textit{M. G. Armentano} et al., Comput. Methods Appl. Mech. Eng. 200, No. 1--4, 178--188 (2010; Zbl 1225.74078) Full Text: DOI
Gardini, Francesca Mixed approximation of eigenvalue problems: A superconvergence result. (English) Zbl 1190.65167 ESAIM, Math. Model. Numer. Anal. 43, No. 5, 853-865 (2009). Reviewer: Norikazu Saito (Tokyo) MSC: 65N25 65N30 35P15 65N12 PDFBibTeX XMLCite \textit{F. Gardini}, ESAIM, Math. Model. Numer. Anal. 43, No. 5, 853--865 (2009; Zbl 1190.65167) Full Text: DOI EuDML
Lin, Qun; Xie, Hehu Asymptotic error expansion and Richardson extrapolation of eigenvalue approximations for second order elliptic problems by the mixed finite element method. (English) Zbl 1201.65202 Appl. Numer. Math. 59, No. 8, 1884-1893 (2009). Reviewer: M. Plum (Karlsruhe) MSC: 65N25 65N30 65L15 65B99 PDFBibTeX XMLCite \textit{Q. Lin} and \textit{H. Xie}, Appl. Numer. Math. 59, No. 8, 1884--1893 (2009; Zbl 1201.65202) Full Text: DOI
Lovadina, Carlo; Lyly, Mikko; Stenberg, Rolf A posteriori estimates for the Stokes eigenvalue problem. (English) Zbl 1169.65109 Numer. Methods Partial Differ. Equations 25, No. 1, 244-257 (2009). Reviewer: Alan L. Andrew (Bundoora) MSC: 65N25 65N15 65N30 35P15 PDFBibTeX XMLCite \textit{C. Lovadina} et al., Numer. Methods Partial Differ. Equations 25, No. 1, 244--257 (2009; Zbl 1169.65109) Full Text: DOI
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 PDFBibTeX XMLCite \textit{Y. Yang} and \textit{Z. Chen}, Sci. China, Ser. A 51, No. 7, 1232--1242 (2008; Zbl 1153.65055) Full Text: DOI
Armentano, María G.; Padra, Claudio A posteriori error estimates for the Steklov eigenvalue problem. (English) Zbl 1140.65078 Appl. Numer. Math. 58, No. 5, 593-601 (2008). Reviewer: Calin Ioan Gheorghiu (Cluj-Napoca) MSC: 65N25 65N30 65N15 35P15 PDFBibTeX XMLCite \textit{M. G. Armentano} and \textit{C. Padra}, Appl. Numer. Math. 58, No. 5, 593--601 (2008; Zbl 1140.65078) Full Text: DOI
Alonso, Ana; Russo, Anahí Dello; Padra, Claudio; Rodríguez, Rodolfo Accurate pressure post-process of a finite element method for elastoacoustics. (English) Zbl 1140.76456 Numer. Math. 98, No. 3, 389-425 (2004). MSC: 76Q05 74F10 74J99 74S05 PDFBibTeX XMLCite \textit{A. Alonso} et al., Numer. Math. 98, No. 3, 389--425 (2004; Zbl 1140.76456) Full Text: DOI
Alonso, A.; Dello Russo, A.; Vampa, V. A posteriori error estimates in finite element acoustic analysis. (English) Zbl 0972.76053 J. Comput. Appl. Math. 117, No. 2, 105-119 (2000). MSC: 76M10 76Q05 65N15 PDFBibTeX XMLCite \textit{A. Alonso} et al., J. Comput. Appl. Math. 117, No. 2, 105--119 (2000; Zbl 0972.76053) Full Text: DOI