Manohar, Ram; Sinha, Rajen Kumar Elliptic reconstruction and a posteriori error estimates for fully discrete semilinear parabolic optimal control problems. (English) Zbl 1499.49020 J. Comput. Math. 40, No. 2, 147-176 (2022). MSC: 49J20 65J15 65N30 PDFBibTeX XMLCite \textit{R. Manohar} and \textit{R. K. Sinha}, J. Comput. Math. 40, No. 2, 147--176 (2022; Zbl 1499.49020) Full Text: DOI
Bernardi, Christine; Orfi, Ajmia Younes A posteriori error analysis of the fully discretized time-dependent coupled Darcy and Stokes equations. (English) Zbl 1419.65053 Comput. Math. Appl. 76, No. 2, 340-360 (2018). MSC: 65M60 65M15 76S05 76D07 65M06 PDFBibTeX XMLCite \textit{C. Bernardi} and \textit{A. Y. Orfi}, Comput. Math. Appl. 76, No. 2, 340--360 (2018; Zbl 1419.65053) Full Text: DOI
Tang, Yuelong; Hua, Yuchun An adaptive finite element algorithm for parabolic optimal control problems. (English) Zbl 1326.65079 Lobachevskii J. Math. 36, No. 1, 48-57 (2015). Reviewer: Basilis Kokkinis (Athens) MSC: 65K10 49J20 49M25 PDFBibTeX XMLCite \textit{Y. Tang} and \textit{Y. Hua}, Lobachevskii J. Math. 36, No. 1, 48--57 (2015; Zbl 1326.65079) Full Text: DOI
Araya, Rodolfo; Venegas, Pablo An a posteriori error estimator for an unsteady advection-diffusion-reaction problem. (English) Zbl 1368.65186 Comput. Math. Appl. 66, No. 12, 2456-2476 (2014). MSC: 65M60 65M12 65M15 35K20 PDFBibTeX XMLCite \textit{R. Araya} and \textit{P. Venegas}, Comput. Math. Appl. 66, No. 12, 2456--2476 (2014; Zbl 1368.65186) Full Text: DOI
Cui, Ming; Yan, Ningning A posteriori error estimate for the Stokes-Darcy system. (English) Zbl 1369.76023 Math. Methods Appl. Sci. 34, No. 9, 1050-1064 (2011). MSC: 76M10 76S05 65N30 PDFBibTeX XMLCite \textit{M. Cui} and \textit{N. Yan}, Math. Methods Appl. Sci. 34, No. 9, 1050--1064 (2011; Zbl 1369.76023) Full Text: DOI
Aboulaich, Rajaa; Achchab, Boujemâa; Darouichi, Aziz A posteriori error estimate for a one-dimensional pollution problem in porous media. (English. Abridged French version) Zbl 1400.76077 C. R., Math., Acad. Sci. Paris 347, No. 19-20, 1217-1222 (2009). MSC: 76S05 76M25 65M08 65M12 PDFBibTeX XMLCite \textit{R. Aboulaich} et al., C. R., Math., Acad. Sci. Paris 347, No. 19--20, 1217--1222 (2009; Zbl 1400.76077) Full Text: DOI
Parés, Núria; Díez, Pedro; Huerta, Antonio Bounds of functional outputs for parabolic problems. I: Exact bounds of the discontinuous Galerkin time discretization. (English) Zbl 1194.65109 Comput. Methods Appl. Mech. Eng. 197, No. 19-20, 1641-1660 (2008). MSC: 65M15 65M60 PDFBibTeX XMLCite \textit{N. Parés} et al., Comput. Methods Appl. Mech. Eng. 197, No. 19--20, 1641--1660 (2008; Zbl 1194.65109) Full Text: DOI
Bernardi, Christine; Girault, Vivette; Rajagopal, Kumbakonam R. Discretization of an unsteady flow through a porous solid modeled by Darcy’s equations. (English) Zbl 1157.76023 Math. Models Methods Appl. Sci. 18, No. 12, 2087-2123 (2008). MSC: 76M10 76M20 76S05 65M15 65M60 PDFBibTeX XMLCite \textit{C. Bernardi} et al., Math. Models Methods Appl. Sci. 18, No. 12, 2087--2123 (2008; Zbl 1157.76023) 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
Bernardi, Christine; Süli, Endre Time and space adaptivity for the second-order wave equation. (English) Zbl 1070.65083 Math. Models Methods Appl. Sci. 15, No. 2, 199-225 (2005). Reviewer: Emil Minchev (Tokyo) MSC: 65M15 65M60 65M50 65M06 35L05 PDFBibTeX XMLCite \textit{C. Bernardi} and \textit{E. Süli}, Math. Models Methods Appl. Sci. 15, No. 2, 199--225 (2005; Zbl 1070.65083) Full Text: DOI
Bernardi, Christine; Verfürth, Rüdiger A posteriori error analysis of the fully discretized time-dependent Stokes equations. (English) Zbl 1079.76042 M2AN, Math. Model. Numer. Anal. 38, No. 3, 437-455 (2004). MSC: 76M10 76M20 76D07 65M15 PDFBibTeX XMLCite \textit{C. Bernardi} and \textit{R. Verfürth}, M2AN, Math. Model. Numer. Anal. 38, No. 3, 437--455 (2004; Zbl 1079.76042) Full Text: DOI Numdam EuDML
Wang, Rong; Keast, Patrick; Muir, Paul A comparison of adaptive software for 1D parabolic PDEs. (English) Zbl 1052.65085 J. Comput. Appl. Math. 169, No. 1, 127-150 (2004). MSC: 65M20 65M50 65M70 35K55 65L80 65M15 65Y15 PDFBibTeX XMLCite \textit{R. Wang} et al., J. Comput. Appl. Math. 169, No. 1, 127--150 (2004; Zbl 1052.65085) Full Text: DOI
Tran, Thanh; Duong, Thanh-Binh A complete analysis for some a posteriori error estimates with the finite element method of lines for a nonlinear parabolic equation. (English) Zbl 1022.65105 Numer. Funct. Anal. Optimization 23, No. 7-8, 891-909 (2002). Reviewer: Emil Minchev (Chiba) MSC: 65M15 35K55 65M12 65M20 65M60 PDFBibTeX XMLCite \textit{T. Tran} and \textit{T.-B. Duong}, Numer. Funct. Anal. Optim. 23, No. 7--8, 891--909 (2002; Zbl 1022.65105) Full Text: DOI
Fröhlich, Jochen; Lang, Jens Two-dimensional cascadic finite element computations of combustion problems. (English) Zbl 0954.76044 Comput. Methods Appl. Mech. Eng. 158, No. 3-4, 255-267 (1998). MSC: 76M10 76V05 92E20 80A25 PDFBibTeX XMLCite \textit{J. Fröhlich} and \textit{J. Lang}, Comput. Methods Appl. Mech. Eng. 158, No. 3--4, 255--267 (1998; Zbl 0954.76044) Full Text: DOI
Angermann, Lutz A posteriori error estimates for approximate solutions of nonlinear equations with weakly stable operators. (English) Zbl 0903.65051 Numer. Funct. Anal. Optimization 18, No. 5-6, 447-459 (1997). Reviewer: E.Emmrich (Magdeburg) MSC: 65J15 65Z05 47J25 65M60 35K55 PDFBibTeX XMLCite \textit{L. Angermann}, Numer. Funct. Anal. Optim. 18, No. 5--6, 447--459 (1997; Zbl 0903.65051) Full Text: DOI
Rao, V. China Venkata; Das, P. C.; Sundararajan, T. An adaptive \(hp\)-version of the finite element method applied to flame propagation problems. (English) Zbl 0901.76037 Int. J. Numer. Methods Eng. 40, No. 17, 3181-3203 (1997). MSC: 76M10 76V05 80A25 PDFBibTeX XMLCite \textit{V. C. V. Rao} et al., Int. J. Numer. Methods Eng. 40, No. 17, 3181--3203 (1997; Zbl 0901.76037) Full Text: DOI
Saad, Mazen; Zhang, Huilong Front tracking for two-phase flow in reservoir simulation by adaptive mesh. (English) Zbl 0895.76061 Numer. Methods Partial Differ. Equations 13, No. 6, 673-697 (1997). MSC: 76M20 76T99 65M50 86A20 PDFBibTeX XMLCite \textit{M. Saad} and \textit{H. Zhang}, Numer. Methods Partial Differ. Equations 13, No. 6, 673--697 (1997; Zbl 0895.76061) Full Text: DOI
Lang, Jens Two-dimensional fully adaptive solutions of reaction-diffusion equations. (English) Zbl 0846.65044 Appl. Numer. Math. 18, No. 1-3, 223-240 (1995). Reviewer: M.Lenard (Kuwait) MSC: 65M20 65L06 65M15 65M50 65L60 35K57 80A25 PDFBibTeX XMLCite \textit{J. Lang}, Appl. Numer. Math. 18, No. 1--3, 223--240 (1995; Zbl 0846.65044) Full Text: DOI
Segeth, Karel A posteriori error estimates for parabolic differential systems solved by the finite element method of lines. (English) Zbl 0822.65068 Appl. Math., Praha 39, No. 6, 415-443 (1994). Reviewer: A.K.Pani (Bombay) MSC: 65M20 65M60 65M15 65M12 35K15 PDFBibTeX XMLCite \textit{K. Segeth}, Appl. Math., Praha 39, No. 6, 415--443 (1994; Zbl 0822.65068) Full Text: EuDML
Verfürth, R. A posteriori error estimation and adaptive mesh-refinement techniques. (English) Zbl 0811.65089 J. Comput. Appl. Math. 50, No. 1-3, 67-83 (1994). Reviewer: V.Makarov (Kiev) MSC: 65N15 65N30 65N50 35J05 PDFBibTeX XMLCite \textit{R. Verfürth}, J. Comput. Appl. Math. 50, No. 1--3, 67--83 (1994; Zbl 0811.65089) Full Text: DOI
Adjerid, Slimane; Flaherty, Joseph E.; Wang, Yun J. A posteriori error estimation with finite element methods of lines for one-dimensional parabolic systems. (English) Zbl 0791.65070 Numer. Math. 65, No. 1, 1-21 (1993). Reviewer: Slimane Adjerid MSC: 65M20 65M60 65M15 35K15 PDFBibTeX XMLCite \textit{S. Adjerid} et al., Numer. Math. 65, No. 1, 1--21 (1993; Zbl 0791.65070) Full Text: DOI EuDML
Strouboulis, T.; Oden, J. T. A posteriori error estimation of finite element approximations in fluid mechanics. (English) Zbl 0711.76061 Comput. Methods Appl. Mech. Eng. 78, No. 2, 201-242 (1990). MSC: 76M10 76R50 PDFBibTeX XMLCite \textit{T. Strouboulis} and \textit{J. T. Oden}, Comput. Methods Appl. Mech. Eng. 78, No. 2, 201--242 (1990; Zbl 0711.76061) Full Text: DOI
Arney, David C.; Flaherty, Joseph E. An adaptive local mesh refinement method for time-dependent partial differential equations. (English) Zbl 0675.65119 Appl. Numer. Math. 5, No. 4, 257-274 (1989). Reviewer: J.Vaníček MSC: 65N50 65M50 65N06 35L65 PDFBibTeX XMLCite \textit{D. C. Arney} and \textit{J. E. Flaherty}, Appl. Numer. Math. 5, No. 4, 257--274 (1989; Zbl 0675.65119) Full Text: DOI
Adjerid, Slimane; Flaherty, Joseph E. Second-order finite element approximations and a posteriori error estimation for two-dimensional parabolic systems. (English) Zbl 0628.65104 Numer. Math. 53, No. 1-2, 183-198 (1988). MSC: 65N30 65N40 65N15 35K50 65L10 65L60 PDFBibTeX XMLCite \textit{S. Adjerid} and \textit{J. E. Flaherty}, Numer. Math. 53, No. 1--2, 183--198 (1988; Zbl 0628.65104) Full Text: DOI EuDML
Adjerid, Slimane; Flaherty, Joseph E. A moving-mesh finite element method with local refinement for parabolic partial differential equations. (English) Zbl 0612.65070 Comput. Methods Appl. Mech. Eng. 55, 3-26 (1986). Reviewer: P.K.Mahanti MSC: 65N30 65N15 65N50 35K20 PDFBibTeX XMLCite \textit{S. Adjerid} and \textit{J. E. Flaherty}, Comput. Methods Appl. Mech. Eng. 55, 3--26 (1986; Zbl 0612.65070) Full Text: DOI
Demkowicz, L.; Oden, J. T.; Strouboulis, T. Adaptive finite elements for flow problems with moving boundaries. I. Variational principles and a posteriori estimates. (English) Zbl 0583.76025 Comput. Methods Appl. Mech. Eng. 46, 217-251 (1984). Reviewer: W.Ames MSC: 76D05 65M60 PDFBibTeX XMLCite \textit{L. Demkowicz} et al., Comput. Methods Appl. Mech. Eng. 46, 217--251 (1984; Zbl 0583.76025) Full Text: DOI
Bieterman, M.; Babuška, Ivo The finite element method for parabolic equations. II. A posteriori error estimation and adaptive approach. (English) Zbl 0534.65073 Numer. Math. 40, 373-406 (1982). Reviewer: D.R.Westbrock MSC: 65N30 65N40 65N15 35K20 PDFBibTeX XMLCite \textit{M. Bieterman} and \textit{I. Babuška}, Numer. Math. 40, 373--406 (1982; Zbl 0534.65073) Full Text: DOI EuDML