Schneider, Matti; Wicht, Daniel Superconvergence of the effective Cauchy stress in computational homogenization of inelastic materials. (English) Zbl 07769192 Int. J. Numer. Methods Eng. 124, No. 4, 959-978 (2023). MSC: 65Mxx 74Qxx 65Nxx PDFBibTeX XMLCite \textit{M. Schneider} and \textit{D. Wicht}, Int. J. Numer. Methods Eng. 124, No. 4, 959--978 (2023; Zbl 07769192) Full Text: DOI OA License
Linot, Alec J.; Graham, Michael D. Dynamics of a data-driven low-dimensional model of turbulent minimal Couette flow. (English) Zbl 07757029 J. Fluid Mech. 973, Paper No. A42, 30 p. (2023). MSC: 76-XX PDFBibTeX XMLCite \textit{A. J. Linot} and \textit{M. D. Graham}, J. Fluid Mech. 973, Paper No. A42, 30 p. (2023; Zbl 07757029) Full Text: DOI arXiv OA License
Gao, Huadong; Qiu, Weifeng A new error analysis and post-processing technique of the lowest-order Raviart-Thomas mixed finite element method for parabolic problems. (English) Zbl 07654113 Comput. Math. Appl. 133, 174-188 (2023). MSC: 65N30 65M60 65N15 35J25 76M10 PDFBibTeX XMLCite \textit{H. Gao} and \textit{W. Qiu}, Comput. Math. Appl. 133, 174--188 (2023; Zbl 07654113) Full Text: DOI
Linot, Alec J.; Burby, Joshua W.; Tang, Qi; Balaprakash, Prasanna; Graham, Michael D.; Maulik, Romit Stabilized neural ordinary differential equations for long-time forecasting of dynamical systems. (English) Zbl 07640581 J. Comput. Phys. 474, Article ID 111838, 14 p. (2023). MSC: 65Mxx 35Bxx 35Kxx PDFBibTeX XMLCite \textit{A. J. Linot} et al., J. Comput. Phys. 474, Article ID 111838, 14 p. (2023; Zbl 07640581) Full Text: DOI arXiv
Shang, Yueqiang; Zhang, Qihui A subgrid stabilizing postprocessed mixed finite element method for the time-dependent Navier-Stokes equations. (English) Zbl 1471.65153 Discrete Contin. Dyn. Syst., Ser. B 26, No. 6, 3119-3142 (2021). MSC: 65M60 35Q30 76D05 65M06 65N30 65M15 65M12 PDFBibTeX XMLCite \textit{Y. Shang} and \textit{Q. Zhang}, Discrete Contin. Dyn. Syst., Ser. B 26, No. 6, 3119--3142 (2021; Zbl 1471.65153) Full Text: DOI
García-Archilla, Bosco; Novo, Julia Error analysis of fully discrete mixed finite element data assimilation schemes for the Navier-Stokes equations. (English) Zbl 1454.65115 Adv. Comput. Math. 46, No. 4, Paper No. 61, 33 p. (2020). MSC: 65M60 65M06 65N30 65M70 65M20 65L06 65M12 65M15 76D05 35Q30 PDFBibTeX XMLCite \textit{B. García-Archilla} and \textit{J. Novo}, Adv. Comput. Math. 46, No. 4, Paper No. 61, 33 p. (2020; Zbl 1454.65115) Full Text: DOI arXiv
García-Archilla, Bosco; Novo, Julia; Titi, Edriss S. Uniform in time error estimates for a finite element method applied to a downscaling data assimilation algorithm for the Navier-Stokes equations. (English) Zbl 1448.65157 SIAM J. Numer. Anal. 58, No. 1, 410-429 (2020). Reviewer: Jürgen Socolowsky (Brandenburg an der Havel) MSC: 65M60 65M12 35Q30 65M15 65M20 76B75 65N30 65M70 PDFBibTeX XMLCite \textit{B. García-Archilla} et al., SIAM J. Numer. Anal. 58, No. 1, 410--429 (2020; Zbl 1448.65157) Full Text: DOI arXiv
Zhang, Qihui; Shang, Yueqiang An Oseen-type post-processed finite element method based on a subgrid model for the time-dependent Navier-Stokes equations. (English) Zbl 1476.76052 Int. J. Comput. Methods 17, No. 4, Article ID 1950002, 24 p. (2020). MSC: 76M10 76D05 65N30 65N22 PDFBibTeX XMLCite \textit{Q. Zhang} and \textit{Y. Shang}, Int. J. Comput. Methods 17, No. 4, Article ID 1950002, 24 p. (2020; Zbl 1476.76052) Full Text: DOI
Durango, Francisco; Novo, Julia Two-grid mixed finite-element approximations to the Navier-Stokes equations based on a Newton-type step. (English) Zbl 1404.65166 J. Sci. Comput. 74, No. 1, 456-473 (2018). MSC: 65M60 76D05 35Q30 65H10 76D07 PDFBibTeX XMLCite \textit{F. Durango} and \textit{J. Novo}, J. Sci. Comput. 74, No. 1, 456--473 (2018; Zbl 1404.65166) Full Text: DOI
Mondaini, Cecilia F.; Titi, Edriss S. Uniform-in-time error estimates for the postprocessing Galerkin method applied to a data assimilation algorithm. (English) Zbl 1384.35067 SIAM J. Numer. Anal. 56, No. 1, 78-110 (2018). Reviewer: Piotr Biler (Wrocław) MSC: 35Q30 76B75 37L65 65M15 65M60 65M70 93C20 93B52 PDFBibTeX XMLCite \textit{C. F. Mondaini} and \textit{E. S. Titi}, SIAM J. Numer. Anal. 56, No. 1, 78--110 (2018; Zbl 1384.35067) Full Text: DOI
Figueras, Jordi-Lluís; de la Llave, Rafael Numerical computations and computer assisted proofs of periodic orbits of the Kuramoto-Sivashinsky equation. (English) Zbl 1370.65047 SIAM J. Appl. Dyn. Syst. 16, No. 2, 834-852 (2017). MSC: 65M22 37K10 37C27 65G40 65M15 PDFBibTeX XMLCite \textit{J.-L. Figueras} and \textit{R. de la Llave}, SIAM J. Appl. Dyn. Syst. 16, No. 2, 834--852 (2017; Zbl 1370.65047) Full Text: DOI arXiv
Sciacca, Vincenzo; Schonbek, M. E.; Sammartino, Marco Long time behavior for a dissipative shallow water model. (English. French summary) Zbl 1383.35174 Ann. Inst. Henri Poincaré, Anal. Non Linéaire 34, No. 3, 731-757 (2017). MSC: 35Q35 35B40 35Q53 76D99 PDFBibTeX XMLCite \textit{V. Sciacca} et al., Ann. Inst. Henri Poincaré, Anal. Non Linéaire 34, No. 3, 731--757 (2017; Zbl 1383.35174) Full Text: DOI arXiv
Wang, Wansheng; Chen, Long; Zhou, Jie Postprocessing mixed finite element methods for solving Cahn-Hilliard equation: methods and error analysis. (English) Zbl 1341.65040 J. Sci. Comput. 67, No. 2, 724-746 (2016). Reviewer: Calin Ioan Gheorghiu (Cluj-Napoca) MSC: 65M60 65M15 65M20 35Q35 65M12 PDFBibTeX XMLCite \textit{W. Wang} et al., J. Sci. Comput. 67, No. 2, 724--746 (2016; Zbl 1341.65040) Full Text: DOI
Pani, Amiya K.; Pany, Ambit K.; Damazio, Pedro; Yuan, Jin Yun A modified nonlinear spectral Galerkin method for the equations of motion arising in the Kelvin-Voigt fluids. (English) Zbl 1356.76218 Appl. Anal. 93, No. 8, 1587-1610 (2014). MSC: 76M22 76A10 65M15 65M12 PDFBibTeX XMLCite \textit{A. K. Pani} et al., Appl. Anal. 93, No. 8, 1587--1610 (2014; Zbl 1356.76218) Full Text: DOI
Liu, Qingfang; Hou, Yanren; Liu, Qingchang A two-level method in space and time for the Navier-Stokes equations. (English) Zbl 1274.76253 Numer. Methods Partial Differ. Equations 29, No. 5, 1504-1521 (2013). MSC: 76M10 76D05 76F65 PDFBibTeX XMLCite \textit{Q. Liu} et al., Numer. Methods Partial Differ. Equations 29, No. 5, 1504--1521 (2013; Zbl 1274.76253) Full Text: DOI
Song, Lina; Hou, Yanren; Zheng, Haibiao Adaptive local postprocessing finite element method for the Navier-Stokes equations. (English) Zbl 1366.76057 J. Sci. Comput. 55, No. 2, 255-267 (2013). MSC: 76M10 65N30 76D05 PDFBibTeX XMLCite \textit{L. Song} et al., J. Sci. Comput. 55, No. 2, 255--267 (2013; Zbl 1366.76057) Full Text: DOI
Strouboulis, Theofanis; Wang, Delin; Babuška, Ivo Superconvergence of elliptic reconstructions of finite element solutions of parabolic problems in domains with piecewise smooth boundaries. (English) Zbl 1354.65198 Comput. Methods Appl. Mech. Eng. 241-244, 128-141 (2012). MSC: 65M60 65M12 PDFBibTeX XMLCite \textit{T. Strouboulis} et al., Comput. Methods Appl. Mech. Eng. 241--244, 128--141 (2012; Zbl 1354.65198) Full Text: DOI
de Frutos, Javier; García-Archilla, Bosco; Novo, Julia Static two-grid mixed finite-element approximations to the Navier-Stokes equations. (English) Zbl 1264.76065 J. Sci. Comput. 52, No. 3, 619-637 (2012). MSC: 76M10 76D05 PDFBibTeX XMLCite \textit{J. de Frutos} et al., J. Sci. Comput. 52, No. 3, 619--637 (2012; Zbl 1264.76065) Full Text: DOI arXiv
de Frutos, Javier; García-Archilla, Bosco; Novo, Julia Optimal error bounds for two-grid schemes applied to the Navier-Stokes equations. (English) Zbl 1426.76244 Appl. Math. Comput. 218, No. 13, 7034-7051 (2012). MSC: 76M10 76D05 65M15 PDFBibTeX XMLCite \textit{J. de Frutos} et al., Appl. Math. Comput. 218, No. 13, 7034--7051 (2012; Zbl 1426.76244) Full Text: DOI arXiv
de Frutos, Javier; García-Archilla, Bosco; Novo, Julia A posteriori error estimations for mixed finite-element approximations to the Navier-Stokes equations. (English) Zbl 1238.76031 J. Comput. Appl. Math. 236, No. 6, 1103-1122 (2011). Reviewer: Calin Ioan Gheorghiu (Cluj-Napoca) MSC: 76M10 76D05 76D07 65M15 65M60 PDFBibTeX XMLCite \textit{J. de Frutos} et al., J. Comput. Appl. Math. 236, No. 6, 1103--1122 (2011; Zbl 1238.76031) Full Text: DOI arXiv
He, Yinnian; Hou, Yanren Galerkin and subspace decomposition methods in space and time for the Navier-Stokes equations. (English) Zbl 1213.35340 Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 74, No. 10, 3218-3231 (2011). MSC: 35Q30 65M60 76D05 65M15 76M10 PDFBibTeX XMLCite \textit{Y. He} and \textit{Y. Hou}, Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 74, No. 10, 3218--3231 (2011; Zbl 1213.35340) Full Text: DOI
Liu, Qingfang; Hou, Yanren A two-level correction method in space and time based on Crank-Nicolson scheme for Navier-Stokes equations. (English) Zbl 1337.76048 Int. J. Comput. Math. 87, No. 11, 2520-2532 (2010). MSC: 76M22 65M06 65M12 PDFBibTeX XMLCite \textit{Q. Liu} and \textit{Y. Hou}, Int. J. Comput. Math. 87, No. 11, 2520--2532 (2010; Zbl 1337.76048) Full Text: DOI
Cao, Dengqing; Wang, Jinlin; Huang, Wenhu A novel order reduction method for nonlinear dynamical system under external periodic excitations. (English) Zbl 1202.37115 Sci. China, Technol. Sci. 53, No. 3, 684-691 (2010). Reviewer: Vasile Marinca (Timişoara) MSC: 37L65 37B55 PDFBibTeX XMLCite \textit{D. Cao} et al., Sci. China, Technol. Sci. 53, No. 3, 684--691 (2010; Zbl 1202.37115) Full Text: DOI
Liu, Qingfang; Hou, Yanren A two-level finite element method for the Navier-Stokes equations based on a new projection. (English) Zbl 1185.76815 Appl. Math. Modelling 34, No. 2, 383-399 (2010). MSC: 76M10 65M60 35Q30 76D05 PDFBibTeX XMLCite \textit{Q. Liu} and \textit{Y. Hou}, Appl. Math. Modelling 34, No. 2, 383--399 (2010; Zbl 1185.76815) Full Text: DOI
Liu, Qingfang; Hou, Yanren A postprocessing mixed finite element method for the Navier-Stokes equations. (English) Zbl 1172.76024 Int. J. Comput. Fluid Dyn. 23, No. 6, 461-475 (2009). MSC: 76M10 76D05 65M12 65M60 PDFBibTeX XMLCite \textit{Q. Liu} and \textit{Y. Hou}, Int. J. Comput. Fluid Dyn. 23, No. 6, 461--475 (2009; Zbl 1172.76024) Full Text: DOI
Yang, Min; Bi, Chunjia; Liu, Jiangguo Postprocessing of a finite volume element method for semilinear parabolic problems. (English) Zbl 1176.65102 ESAIM, Math. Model. Numer. Anal. 43, No. 5, 957 (2009). Reviewer: Ruxandra Stavre (Bucureşti) MSC: 65M08 35K58 35K61 PDFBibTeX XMLCite \textit{M. Yang} et al., ESAIM, Math. Model. Numer. Anal. 43, No. 5, 957 (2009; Zbl 1176.65102) Full Text: DOI EuDML
Yang, Min; Song, Huailing A postprocessing finite volume element method for time-dependent Stokes equations. (English) Zbl 1165.76028 Appl. Numer. Math. 59, No. 8, 1922-1932 (2009). MSC: 76M10 76M12 76D07 PDFBibTeX XMLCite \textit{M. Yang} and \textit{H. Song}, Appl. Numer. Math. 59, No. 8, 1922--1932 (2009; Zbl 1165.76028) Full Text: DOI
Andrianov, I. V. Asymptotic construction of nonlinear normal modes for continuous systems. (English) Zbl 1170.74331 Nonlinear Dyn. 51, No. 1-2, 99-109 (2008). MSC: 74H10 74H45 74K10 PDFBibTeX XMLCite \textit{I. V. Andrianov}, Nonlinear Dyn. 51, No. 1--2, 99--109 (2008; Zbl 1170.74331) Full Text: DOI
Tachim Medjo, T.; Temam, R. A two-grid finite difference method for the primitive equations of the ocean. (English) Zbl 1142.76368 Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 69, No. 3, 1034-1056 (2008). MSC: 76D55 65N12 49K35 PDFBibTeX XMLCite \textit{T. Tachim Medjo} and \textit{R. Temam}, Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 69, No. 3, 1034--1056 (2008; Zbl 1142.76368) Full Text: DOI
de Frutos, Javier; García-Archilla, Bosco; Novo, Julia A posteriori error estimates for fully discrete nonlinear parabolic problems. (English) Zbl 1173.65335 Comput. Methods Appl. Mech. Eng. 196, No. 35-36, 3462-3474 (2007). MSC: 65M15 65M60 PDFBibTeX XMLCite \textit{J. de Frutos} et al., Comput. Methods Appl. Mech. Eng. 196, No. 35--36, 3462--3474 (2007; Zbl 1173.65335) Full Text: DOI
Sinha, S. C.; Redkar, Sangram; Butcher, Eric A. On macromodeling of nonlinear systems with time periodic coefficients. (English) Zbl 1112.34023 Commun. Nonlinear Sci. Numer. Simul. 11, No. 4, 510-530 (2006). Reviewer: Smail Djebali (Algiers) MSC: 34C20 34C45 93A30 PDFBibTeX XMLCite \textit{S. C. Sinha} et al., Commun. Nonlinear Sci. Numer. Simul. 11, No. 4, 510--530 (2006; Zbl 1112.34023) Full Text: DOI
He, Yinnian; Liu, Kam-Moon Multi-level spectral Galerkin method for the Navier-Stokes equations. II: Time discretization. (English) Zbl 1331.65146 Adv. Comput. Math. 25, No. 4, 403-433 (2006). MSC: 65M70 35Q30 76D05 76M22 PDFBibTeX XMLCite \textit{Y. He} and \textit{K.-M. Liu}, Adv. Comput. Math. 25, No. 4, 403--433 (2006; Zbl 1331.65146) Full Text: DOI
Laing, Carlo R. On the application of “equation-free modelling” to neural systems. (English) Zbl 1119.92014 J. Comput. Neurosci. 20, No. 1, 5-23 (2006). MSC: 92C20 37N25 PDFBibTeX XMLCite \textit{C. R. Laing}, J. Comput. Neurosci. 20, No. 1, 5--23 (2006; Zbl 1119.92014) Full Text: DOI
Sinha, S. C.; Redkar, Sangram; Deshmukh, Venkatesh; Butcher, Eric A. Order reduction of parametrically excited nonlinear systems: Techniques and applications. (English) Zbl 1101.70013 Nonlinear Dyn. 41, No. 1-3, 237-273 (2005). Reviewer: Hans Troger (Wien) MSC: 70K28 70K30 34C20 PDFBibTeX XMLCite \textit{S. C. Sinha} et al., Nonlinear Dyn. 41, No. 1--3, 237--273 (2005; Zbl 1101.70013) Full Text: DOI
He, Yinnian; Liu, Kam-Moon; Sun, Weiwei Multi-level spectral Galerkin method for the Navier-Stokes problem. I: Spatial discretization. (English) Zbl 1096.65099 Numer. Math. 101, No. 3, 501-522 (2005). Reviewer: Hermann G. Matthies (Braunschweig) MSC: 65M60 65M70 35Q30 65M55 76D05 65M12 76M22 PDFBibTeX XMLCite \textit{Y. He} et al., Numer. Math. 101, No. 3, 501--522 (2005; Zbl 1096.65099) Full Text: DOI
Lee, C. H.; Tran, H. T. Reduced-order-based feedback control of the Kuramoto–Sivashinsky equation. (English) Zbl 1107.93028 J. Comput. Appl. Math. 173, No. 1, 1-19 (2005). MSC: 93D15 76D55 93C20 35Q35 PDFBibTeX XMLCite \textit{C. H. Lee} and \textit{H. T. Tran}, J. Comput. Appl. Math. 173, No. 1, 1--19 (2005; Zbl 1107.93028) Full Text: DOI
García-Archilla, Bosco; Novo, Julia; Titi, Edriss S. Postprocessing Fourier spectral methods: The case of smooth solutions. (English) Zbl 1012.65102 Appl. Numer. Math. 43, No. 3, 191-209 (2002). MSC: 65M70 35K90 65M55 PDFBibTeX XMLCite \textit{B. García-Archilla} et al., Appl. Numer. Math. 43, No. 3, 191--209 (2002; Zbl 1012.65102) Full Text: DOI
He, Yinnian; Mattheij, R. M. M. Stability and convergence of the reform postprocessing Galerkin method. (English) Zbl 0976.65085 Nonlinear Anal., Real World Appl. 1, No. 4, 517-533 (2000). Reviewer: Karel Najzar (Praha) MSC: 65M12 34G20 65L60 65J05 65M60 35Q30 PDFBibTeX XMLCite \textit{Y. He} and \textit{R. M. M. Mattheij}, Nonlinear Anal., Real World Appl. 1, No. 4, 517--533 (2000; Zbl 0976.65085) Full Text: DOI
de Frutos, Javier; Novo, Julia An enhanced pseudospectral Chebyshev method for dissipative partial differential equations. (English) Zbl 0944.65108 J. Comput. Appl. Math. 115, No. 1-2, 137-150 (2000). MSC: 65M70 65M12 35K57 35Q53 PDFBibTeX XMLCite \textit{J. de Frutos} and \textit{J. Novo}, J. Comput. Appl. Math. 115, No. 1--2, 137--150 (2000; Zbl 0944.65108) Full Text: DOI
Laing, Carlo R.; McRobie, Allan; Thompson, J. M. T. The post-processed Galerkin method applied to nonlinear shell vibrations. (English) Zbl 0942.74079 Dyn. Stab. Syst. 14, No. 2, 163-181 (1999). MSC: 74S30 74S20 74H45 74K25 PDFBibTeX XMLCite \textit{C. R. Laing} et al., Dyn. Stab. Syst. 14, No. 2, 163--181 (1999; Zbl 0942.74079) Full Text: DOI
García-Archilla, Bosco; Novo, Julia; Titi, Edriss S. An approximate inertial manifolds approach to postprocessing the Galerkin method for the Navier-Stokes equations. (English) Zbl 0930.76063 Math. Comput. 68, No. 227, 893-911 (1999). MSC: 76M25 76D05 PDFBibTeX XMLCite \textit{B. García-Archilla} et al., Math. Comput. 68, No. 227, 893--911 (1999; Zbl 0930.76063) Full Text: DOI
Costa, Bruno; Dettori, Lucia Fourier collocation splittings for partial differential equations. (English) Zbl 0922.65070 J. Comput. Phys. 142, No. 2, 562-580 (1998). Reviewer: H.Marcinkowska (Wrocław) MSC: 65M70 65M60 35Q53 35K57 PDFBibTeX XMLCite \textit{B. Costa} and \textit{L. Dettori}, J. Comput. Phys. 142, No. 2, 562--580 (1998; Zbl 0922.65070) Full Text: DOI