Akuamoah, Saviour Worlanyo; Seadawy, Aly R. Application of direct extended modified algebraic method of Bogoyavlenskii equation on lower and upper bounds in managing and optimizing queues. (English) Zbl 1443.60080 Int. J. Mod. Phys. B 34, No. 18, Article ID 2050166, 11 p. (2020). MSC: 60K25 35R60 35A25 PDFBibTeX XMLCite \textit{S. W. Akuamoah} and \textit{A. R. Seadawy}, Int. J. Mod. Phys. B 34, No. 18, Article ID 2050166, 11 p. (2020; Zbl 1443.60080) Full Text: DOI
Parish, Eric J.; Carlberg, Kevin T. Time-series machine-learning error models for approximate solutions to parameterized dynamical systems. (English) Zbl 1442.65446 Comput. Methods Appl. Mech. Eng. 365, Article ID 112990, 43 p. (2020). MSC: 65P99 70-08 62M10 62H30 PDFBibTeX XMLCite \textit{E. J. Parish} and \textit{K. T. Carlberg}, Comput. Methods Appl. Mech. Eng. 365, Article ID 112990, 43 p. (2020; Zbl 1442.65446) Full Text: DOI arXiv
Duval, M.; Lozinski, A.; Passieux, J. C.; Salaün, M. Residual error based adaptive mesh refinement with the non-intrusive patch algorithm. (English) Zbl 1439.65159 Comput. Methods Appl. Mech. Eng. 329, 118-143 (2018). MSC: 65N30 65N50 PDFBibTeX XMLCite \textit{M. Duval} et al., Comput. Methods Appl. Mech. Eng. 329, 118--143 (2018; Zbl 1439.65159) Full Text: DOI Link
Darrigrand, Vincent; Pardo, David; Muga, Ignacio Goal-oriented adaptivity using unconventional error representations for the 1D Helmholtz equation. (English) Zbl 1443.65322 Comput. Math. Appl. 69, No. 9, 964-979 (2015). MSC: 65N30 65N50 78A25 PDFBibTeX XMLCite \textit{V. Darrigrand} et al., Comput. Math. Appl. 69, No. 9, 964--979 (2015; Zbl 1443.65322) Full Text: DOI
Rey, Valentine; Rey, Christian; Gosselet, Pierre A strict error bound with separated contributions of the discretization and of the iterative solver in non-overlapping domain decomposition methods. (English) Zbl 1296.65167 Comput. Methods Appl. Mech. Eng. 270, 293-303 (2014). MSC: 65N30 65N55 65N15 65N22 PDFBibTeX XMLCite \textit{V. Rey} et al., Comput. Methods Appl. Mech. Eng. 270, 293--303 (2014; Zbl 1296.65167) Full Text: DOI arXiv
Richter, Thomas Michael Goal-oriented error estimation for fluid-structure interaction problems. (English) Zbl 1253.74037 Comput. Methods Appl. Mech. Eng. 223-224, 28-42 (2012). MSC: 74F10 74S05 76F65 65M60 PDFBibTeX XMLCite \textit{T. M. Richter}, Comput. Methods Appl. Mech. Eng. 223--224, 28--42 (2012; Zbl 1253.74037) Full Text: DOI
Ammar, A.; Chinesta, F.; Diez, P.; Huerta, A. An error estimator for separated representations of highly multidimensional models. (English) Zbl 1231.74503 Comput. Methods Appl. Mech. Eng. 199, No. 25-28, 1872-1880 (2010). MSC: 74S99 76M99 65N15 00A71 PDFBibTeX XMLCite \textit{A. Ammar} et al., Comput. Methods Appl. Mech. Eng. 199, No. 25--28, 1872--1880 (2010; Zbl 1231.74503) Full Text: DOI Link
Fang, F.; Pain, C. C.; Navon, I. M.; Gorman, G. J.; Piggott, M. D.; Allison, P. A.; Goddard, A. J. H. A POD goal-oriented error measure for mesh optimization. (English) Zbl 1425.65096 Int. J. Numer. Methods Fluids 63, No. 2, 185-206 (2010). MSC: 65M15 65M50 86A05 PDFBibTeX XMLCite \textit{F. Fang} et al., Int. J. Numer. Methods Fluids 63, No. 2, 185--206 (2010; Zbl 1425.65096) Full Text: DOI
Cheng, Zhong; Ghomeshi, Shahin; Paraschivoiu, Marius Bounds on outputs of the exact weak solution of the three-dimensional Stokes problem. (English) Zbl 1270.35362 Int. J. Numer. Methods Fluids 61, No. 10, 1098-1131 (2009). MSC: 35Q35 35C05 35D30 76D05 PDFBibTeX XMLCite \textit{Z. Cheng} et al., Int. J. Numer. Methods Fluids 61, No. 10, 1098--1131 (2009; Zbl 1270.35362) Full Text: DOI Link
Pardo, David; García-Castillo, Luis E.; Demkowicz, Leszek F.; Torres-Verdín, Carlos A two-dimensional self-adaptive \(hp\) finite element method for the characterization of waveguide discontinuities. II: Goal-oriented \(hp\)-adaptivity. (English) Zbl 1173.78321 Comput. Methods Appl. Mech. Eng. 196, No. 49-52, 4811-4822 (2007). MSC: 78M10 78A50 PDFBibTeX XMLCite \textit{D. Pardo} et al., Comput. Methods Appl. Mech. Eng. 196, No. 49--52, 4811--4822 (2007; Zbl 1173.78321) Full Text: DOI
Choi, Hae-Won; Paraschivoiu, Marius Adaptive domain decomposition for the bound method: application to the incompressible Navier-Stokes and energy equations in three space dimensions. (English) Zbl 1173.76334 Comput. Methods Appl. Mech. Eng. 196, No. 8, 1484-1497 (2007). MSC: 76M10 76D05 65N55 PDFBibTeX XMLCite \textit{H.-W. Choi} and \textit{M. Paraschivoiu}, Comput. Methods Appl. Mech. Eng. 196, No. 8, 1484--1497 (2007; Zbl 1173.76334) Full Text: DOI
Pardo, D.; Demkowicz, L.; Torres-Verdín, C.; Paszynski, M. A self-adaptive goal-oriented \(hp\)-finite element method with electromagnetic applications. II: Electrodynamics. (English) Zbl 1173.78320 Comput. Methods Appl. Mech. Eng. 196, No. 37-40, 3585-3597 (2007). MSC: 78M10 PDFBibTeX XMLCite \textit{D. Pardo} et al., Comput. Methods Appl. Mech. Eng. 196, No. 37--40, 3585--3597 (2007; Zbl 1173.78320) Full Text: DOI
Billade, Nilesh; Vemaganti, Kumar Hierarchical models of thin elastic structures: overview and recent advances in error estimation and adaptivity. (English) Zbl 1173.74400 Comput. Methods Appl. Mech. Eng. 196, No. 37-40, 3508-3523 (2007). MSC: 74S05 74K99 PDFBibTeX XMLCite \textit{N. Billade} and \textit{K. Vemaganti}, Comput. Methods Appl. Mech. Eng. 196, No. 37--40, 3508--3523 (2007; Zbl 1173.74400) Full Text: DOI
Grätsch, Thomas; Bathe, Klaus-Jürgen Goal-oriented error estimation in the analysis of fluid flows with structural interactions. (English) Zbl 1122.76055 Comput. Methods Appl. Mech. Eng. 195, No. 41-43, 5673-5684 (2006). MSC: 76M10 76D05 74F10 PDFBibTeX XMLCite \textit{T. Grätsch} and \textit{K.-J. Bathe}, Comput. Methods Appl. Mech. Eng. 195, No. 41--43, 5673--5684 (2006; Zbl 1122.76055) Full Text: DOI
Power, P. W.; Pain, C. C.; Piggott, M. D.; Fang, F.; Gorman, G. J.; Umpleby, A. P.; Goddard, A. J. H.; Navon, I. M. Adjoint a posteriori error measures for anisotropic mesh optimisation. (English) Zbl 1206.65250 Comput. Math. Appl. 52, No. 8-9, 1213-1242 (2006). MSC: 65N50 65N15 PDFBibTeX XMLCite \textit{P. W. Power} et al., Comput. Math. Appl. 52, No. 8--9, 1213--1242 (2006; Zbl 1206.65250) Full Text: DOI
Grätsch, T.; Hartmann, F. Pointwise error estimation and adaptivity for the finite element method using fundamental solutions. (English) Zbl 1103.74052 Comput. Mech. 37, No. 5, 394-407 (2006). MSC: 74S05 74B05 65N15 PDFBibTeX XMLCite \textit{T. Grätsch} and \textit{F. Hartmann}, Comput. Mech. 37, No. 5, 394--407 (2006; Zbl 1103.74052) Full Text: DOI
Bertsimas, Dimitris; Caramanis, Constantine Bounds on linear PDEs via semidefinite optimization. (English) Zbl 1099.90063 Math. Program. 108, No. 1 (A), 135-158 (2006). MSC: 90C34 35F99 PDFBibTeX XMLCite \textit{D. Bertsimas} and \textit{C. Caramanis}, Math. Program. 108, No. 1 (A), 135--158 (2006; Zbl 1099.90063) Full Text: DOI Link
Parés, N.; Bonet, J.; Huerta, A.; Peraire, J. The computation of bounds for linear-functional outputs of weak solutions to the two-dimensional elasticity equations. (English) Zbl 1193.74041 Comput. Methods Appl. Mech. Eng. 195, No. 4-6, 406-429 (2006). MSC: 74G15 65N30 74S05 35D30 PDFBibTeX XMLCite \textit{N. Parés} et al., Comput. Methods Appl. Mech. Eng. 195, No. 4--6, 406--429 (2006; Zbl 1193.74041) Full Text: DOI Link
Oden, J. Tinsley; Prudhomme, Serge; Demkowicz, Leszek A posteriori error estimation for acoustic wave propagation problems. (English) Zbl 1145.76033 Arch. Comput. Methods Eng. 12, No. 4, 343-389 (2005). MSC: 76M10 76M15 76Q05 65N15 76-02 PDFBibTeX XMLCite \textit{J. T. Oden} et al., Arch. Comput. Methods Eng. 12, No. 4, 343--389 (2005; Zbl 1145.76033) Full Text: DOI
Šolín, P.; Demkowicz, L. Goal-oriented \(hp\)-adaptivity for elliptic problems. (English) Zbl 1044.65082 Comput. Methods Appl. Mech. Eng. 193, No. 6-8, 449-468 (2004). MSC: 65N30 35J05 35Q60 78A40 78A50 78M10 PDFBibTeX XMLCite \textit{P. Šolín} and \textit{L. Demkowicz}, Comput. Methods Appl. Mech. Eng. 193, No. 6--8, 449--468 (2004; Zbl 1044.65082) Full Text: DOI
Maday, Yvon; Turinici, Gabriel Error bars and quadratically convergent methods for the numerical simulation of the Hartree-Fock equations. (English) Zbl 1027.81043 Numer. Math. 94, No. 4, 739-770 (2003). MSC: 81V55 81-08 81Q05 65G99 35Q40 81Q15 PDFBibTeX XMLCite \textit{Y. Maday} and \textit{G. Turinici}, Numer. Math. 94, No. 4, 739--770 (2003; Zbl 1027.81043) Full Text: DOI HAL
Walsh, Timothy; Demkowicz, Leszek \(hp\) boundary element modeling of the external human auditory system – goal-oriented adaptivity with multiple load vectors. (English) Zbl 1083.76561 Comput. Methods Appl. Mech. Eng. 192, No. 1-2, 125-146 (2003). MSC: 76M15 76Q05 92C10 PDFBibTeX XMLCite \textit{T. Walsh} and \textit{L. Demkowicz}, Comput. Methods Appl. Mech. Eng. 192, No. 1--2, 125--146 (2003; Zbl 1083.76561) Full Text: DOI
Choi, Hae-Won; Paraschivoiu, Marius A posteriori finite element output bounds with adaptive mesh refinement: Application to a heat transfer problem in a three-dimensional rectangular duct. (English) Zbl 1099.76515 Comput. Methods Appl. Mech. Eng. 191, No. 43, 4905-4925 (2002). MSC: 76M10 76R99 80A20 80M10 PDFBibTeX XMLCite \textit{H.-W. Choi} and \textit{M. Paraschivoiu}, Comput. Methods Appl. Mech. Eng. 191, No. 43, 4905--4925 (2002; Zbl 1099.76515) Full Text: DOI
Bonet, J.; Huerta, A.; Peraire, J. The efficient computation of bounds for functionals of finite element solutions in large strain elasticity. (English) Zbl 1099.74543 Comput. Methods Appl. Mech. Eng. 191, No. 43, 4807-4826 (2002). MSC: 74S05 74B20 PDFBibTeX XMLCite \textit{J. Bonet} et al., Comput. Methods Appl. Mech. Eng. 191, No. 43, 4807--4826 (2002; Zbl 1099.74543) Full Text: DOI
Patera, Anthony T.; Rønquist, Einar M. A general output bound result: application to discretization and iteration error estimation and control. (English) Zbl 1012.65110 Math. Models Methods Appl. Sci. 11, No. 4, 685-712 (2001). MSC: 65N15 65N55 65N30 35J05 65F10 65F35 PDFBibTeX XMLCite \textit{A. T. Patera} and \textit{E. M. Rønquist}, Math. Models Methods Appl. Sci. 11, No. 4, 685--712 (2001; Zbl 1012.65110) Full Text: DOI
Machiels, L.; Peraire, J.; Patera, A. T. A posteriori finite-element output bounds for the incompressible Navier-Stokes equations: Application to a natural convection problem. (English) Zbl 1002.76069 J. Comput. Phys. 172, No. 2, 401-425 (2001). MSC: 76M10 76D05 76R10 80A20 65N15 PDFBibTeX XMLCite \textit{L. Machiels} et al., J. Comput. Phys. 172, No. 2, 401--425 (2001; Zbl 1002.76069) Full Text: DOI
Oden, J. T.; Prudhomme, S. Goal-oriented error estimation and adaptivity for the finite element method. (English) Zbl 0987.65110 Comput. Math. Appl. 41, No. 5-6, 735-756 (2001). Reviewer: Prabhat Kumar Mahanti (New Brunswick) MSC: 65N15 65N30 35J25 PDFBibTeX XMLCite \textit{J. T. Oden} and \textit{S. Prudhomme}, Comput. Math. Appl. 41, No. 5--6, 735--756 (2001; Zbl 0987.65110) Full Text: DOI
Machiels, L.; Maday, Y.; Patera, A. T. Output bounds for reduced-order approximations of elliptic partial differential equations. (English) Zbl 0984.65118 Comput. Methods Appl. Mech. Eng. 190, No. 26-27, 3413-3426 (2001). MSC: 65N30 65N12 65N15 35J25 80A20 80M10 PDFBibTeX XMLCite \textit{L. Machiels} et al., Comput. Methods Appl. Mech. Eng. 190, No. 26--27, 3413--3426 (2001; Zbl 0984.65118) Full Text: DOI
Machiels, L. A posteriori finite element bounds for output functionals of discontinuous Galerkin discretizations of parabolic problems. (English) Zbl 0984.65100 Comput. Methods Appl. Mech. Eng. 190, No. 26-27, 3401-3411 (2001). MSC: 65M60 65M15 35K15 80M10 80A20 PDFBibTeX XMLCite \textit{L. Machiels}, Comput. Methods Appl. Mech. Eng. 190, No. 26--27, 3401--3411 (2001; Zbl 0984.65100) Full Text: DOI
Maday, Yvon; Patera, Anthony T. Numerical analysis of a posteriori finite element bounds for linear functional outputs. (English) Zbl 1012.65109 Math. Models Methods Appl. Sci. 10, No. 5, 785-799 (2000). MSC: 65N15 65N30 35J25 PDFBibTeX XMLCite \textit{Y. Maday} and \textit{A. T. Patera}, Math. Models Methods Appl. Sci. 10, No. 5, 785--799 (2000; Zbl 1012.65109) Full Text: DOI
Peraire, Jaume; Patera, Anthony T. Asymptotic a posteriori finite element bounds for the outputs of noncoercive problems: The Helmholtz and Burgers equations. (English) Zbl 0943.65124 Comput. Methods Appl. Mech. Eng. 171, No. 1-2, 77-86 (1999). Reviewer: Thomas Sonar (Braunschweig) MSC: 65N15 65N30 35J65 35Q53 PDFBibTeX XMLCite \textit{J. Peraire} and \textit{A. T. Patera}, Comput. Methods Appl. Mech. Eng. 171, No. 1--2, 77--86 (1999; Zbl 0943.65124) Full Text: DOI
Prudhomme, S.; Oden, J. T. On goal-oriented error estimation for elliptic problems: Application to the control of pointwise errors. (English) Zbl 0945.65123 Comput. Methods Appl. Mech. Eng. 176, No. 1-4, 313-331 (1999). Reviewer: A.Galántai (Miskolc-Egyetemvaros) MSC: 65N15 65N30 35J25 PDFBibTeX XMLCite \textit{S. Prudhomme} and \textit{J. T. Oden}, Comput. Methods Appl. Mech. Eng. 176, No. 1--4, 313--331 (1999; Zbl 0945.65123) Full Text: DOI
Ladevèze, P.; Rougeot, Ph.; Blanchard, P.; Moreau, J. P. Local error estimators for finite element linear analysis. (English) Zbl 0967.74066 Comput. Methods Appl. Mech. Eng. 176, No. 1-4, 231-246 (1999). Reviewer: Ladislav Prášek (Plzeň) MSC: 74S05 65N30 PDFBibTeX XMLCite \textit{P. Ladevèze} et al., Comput. Methods Appl. Mech. Eng. 176, No. 1--4, 231--246 (1999; Zbl 0967.74066) Full Text: DOI
Babuška, I.; Strouboulis, T.; Gangaraj, S. K. Guaranteed computable bounds for the exact error in the finite element solution. I: One-dimensional model problem. (English) Zbl 0936.65094 Comput. Methods Appl. Mech. Eng. 176, No. 1-4, 51-79 (1999). Reviewer: D.Petcu (Timişoara) MSC: 65L70 65L60 65L10 34B15 PDFBibTeX XMLCite \textit{I. Babuška} et al., Comput. Methods Appl. Mech. Eng. 176, No. 1--4, 51--79 (1999; Zbl 0936.65094) Full Text: DOI
Paraschivoiu, Marius; Peraire, Jaime; Patera, Anthony T. A posteriori finite element bounds for linear-functional outputs of elliptic partial differential equations. (English) Zbl 0907.65102 Comput. Methods Appl. Mech. Eng. 150, No. 1-4, 289-312 (1997). MSC: 65N15 65N30 35J25 PDFBibTeX XMLCite \textit{M. Paraschivoiu} et al., Comput. Methods Appl. Mech. Eng. 150, No. 1--4, 289--312 (1997; Zbl 0907.65102) Full Text: DOI