Hunter, Thomas P.; Hulshoff, Steven J. SuperAdjoint: super-resolution neural networks in adjoint-based error estimation. (English) Zbl 1545.76089 J. Comput. Appl. Math. 442, Article ID 115722, 15 p. (2024). MSC: 76M99 76M10 76D99 68T07 × Cite Format Result Cite Review PDF Full Text: DOI
Chamoin, Ludovic; Legoll, Frédéric An introductory review on a posteriori error estimation in finite element computations. (English) Zbl 1528.65104 SIAM Rev. 65, No. 4, 963-1028 (2023). Reviewer: Bülent Karasözen (Ankara) MSC: 65N30 65N15 65B05 65N12 65N50 65-02 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Granzow, Brian N.; Seidl, D. Thomas; Bond, Stephen D. Linearization errors in discrete goal-oriented error estimation. (English) Zbl 1539.65171 Comput. Methods Appl. Mech. Eng. 416, Article ID 116364, 24 p. (2023). MSC: 65N30 65N15 65N50 74S05 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Becker, Roland; Brunner, Maximilian; Innerberger, Michael; Melenk, Jens Markus; Praetorius, Dirk Rate-optimal goal-oriented adaptive FEM for semilinear elliptic PDEs. (English) Zbl 1524.65754 Comput. Math. Appl. 118, 18-35 (2022). MSC: 65N30 65N50 65N12 65N15 35J25 35J61 × Cite Format Result Cite Review PDF Full Text: DOI
Houston, Paul; Rourke, Connor J.; van der Zee, Kristoffer G. Linearization of the travel time functional in porous media flows. (English) Zbl 1490.65198 SIAM J. Sci. Comput. 44, No. 3, B531-B557 (2022). MSC: 65M60 65M15 65M50 76S05 × Cite Format Result Cite Review PDF Full Text: DOI arXiv Link
Yu, Peng; Bordas, Stéphane Pierre Alain; Kerfriden, Pierre Adaptive isogeometric analysis for transient dynamics: space-time refinement based on hierarchical a-posteriori error estimations. (English) Zbl 1507.74524 Comput. Methods Appl. Mech. Eng. 394, Article ID 114774, 35 p. (2022). MSC: 74S05 65N30 74H45 74S22 × Cite Format Result Cite Review PDF Full Text: DOI
Parés, N.; Nguyen, N. C.; Díez, P.; Peraire, J. A posteriori goal-oriented bounds for the Poisson problem using potential and equilibrated flux reconstructions: application to the hybridizable discontinuous Galerkin method. (English) Zbl 1507.65249 Comput. Methods Appl. Mech. Eng. 386, Article ID 114088, 29 p. (2021). MSC: 65N30 65N50 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Chamoin, Ludovic; Legoll, Frédéric Goal-oriented error estimation and adaptivity in MsFEM computations. (English) Zbl 1477.35258 Comput. Mech. 67, No. 4, 1201-1228 (2021); correction ibid. 68, No. 1, 229-230 (2021). MSC: 35Q74 74E30 74S05 65N30 65N15 35J15 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Wick, Thomas Dual-weighted residual a posteriori error estimates for a penalized phase-field slit discontinuity problem. (English) Zbl 1490.74095 Comput. Methods Appl. Math. 21, No. 3, 693-707 (2021). MSC: 74R10 65N30 65N50 49M15 35Q74 × Cite Format Result Cite Review PDF Full Text: DOI
Bespalov, Alex; Rocchi, Leonardo; Silvester, David T-IFISS: a toolbox for adaptive FEM computation. (English) Zbl 1524.65004 Comput. Math. Appl. 81, 373-390 (2021). MSC: 65-04 65N30 65N15 65N50 35J25 35R60 97M50 × Cite Format Result Cite Review PDF Full Text: DOI arXiv Link
Smetana, Kathrin; Zahm, Olivier Randomized residual-based error estimators for the proper generalized decomposition approximation of parametrized problems. (English) Zbl 1548.65395 Int. J. Numer. Methods Eng. 121, No. 23, 5153-5177 (2020). MSC: 65N99 × Cite Format Result Cite Review PDF Full Text: DOI arXiv Link
Larion, Ygee; Zlotnik, Sergio; Massart, Thierry J.; Díez, Pedro Building a certified reduced basis for coupled thermo-hydro-mechanical systems with goal-oriented error estimation. (English) Zbl 1466.74026 Comput. Mech. 66, No. 3, 559-573 (2020). MSC: 74L10 74F10 74F05 74S05 76S05 × Cite Format Result Cite Review PDF Full Text: DOI Link
Tirvaudey, Marie; Chamoin, Ludovic; Bouclier, Robin; Passieux, Jean-Charles A posteriori error estimation and adaptivity in non-intrusive couplings between concurrent models. (English) Zbl 1442.74239 Comput. Methods Appl. Mech. Eng. 367, Article ID 113104, 27 p. (2020). MSC: 74S05 65N30 65N15 × Cite Format Result Cite Review PDF Full Text: DOI
Porcù, Roberto; Chiaramonte, Maurizio M. Orthogonality constrained gradient reconstruction for superconvergent linear functionals. (English) Zbl 1447.65159 BIT 60, No. 2, 465-479 (2020). Reviewer: Bülent Karasözen (Ankara) MSC: 65N30 65N15 65N12 65N50 35J15 × Cite Format Result Cite Review PDF Full Text: DOI Link
Rabizadeh, Ehsan; Bagherzadeh, Amir Saboor; Anitescu, Cosmin; Alajlan, Naif; Rabczuk, Timon Pointwise dual weighted residual based goal-oriented a posteriori error estimation and adaptive mesh refinement in 2D/3D thermo-mechanical multifield problems. (English) Zbl 1441.74009 Comput. Methods Appl. Mech. Eng. 359, Article ID 112666, 43 p. (2020). MSC: 74A15 65Z05 × Cite Format Result Cite Review PDF Full Text: DOI
Scarabosio, Laura; Wohlmuth, Barbara; Oden, J. Tinsley; Faghihi, Danial Goal-oriented adaptive modeling of random heterogeneous media and model-based multilevel Monte Carlo methods. (English) Zbl 1443.65008 Comput. Math. Appl. 78, No. 8, 2700-2718 (2019). MSC: 65C05 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Endtmayer, Bernhard; Langer, Ulrich; Wick, Thomas Multigoal-oriented error estimates for non-linear problems. (English) Zbl 1435.65200 J. Numer. Math. 27, No. 4, 215-236 (2019). MSC: 65N30 65M60 49M15 35Q74 65N15 65K10 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Di Stolfo, Paolo; Rademacher, Andreas; Schröder, Andreas Dual weighted residual error estimation for the finite cell method. (English) Zbl 1476.65331 J. Numer. Math. 27, No. 2, 101-122 (2019). MSC: 65N85 65N15 × Cite Format Result Cite Review PDF Full Text: DOI
Smetana, Kathrin; Zahm, Olivier; Patera, Anthony T. Randomized residual-based error estimators for parametrized equations. (English) Zbl 1411.65148 SIAM J. Sci. Comput. 41, No. 2, A900-A926 (2019). MSC: 65N15 65C05 65N30 68Q25 62G15 × Cite Format Result Cite Review PDF Full Text: DOI arXiv HAL
Li, Harriet; Garg, Vikram V.; Willcox, Karen Model adaptivity for goal-oriented inference using adjoints. (English) Zbl 1439.74502 Comput. Methods Appl. Mech. Eng. 331, 1-22 (2018). MSC: 74S99 65N21 74G75 × Cite Format Result Cite Review PDF Full Text: DOI Link
Weißer, Steffen; Wick, Thomas The dual-weighted residual estimator realized on polygonal meshes. (English) Zbl 1422.65417 Comput. Methods Appl. Math. 18, No. 4, 753-776 (2018). Reviewer: Dana Černá (Liberec) MSC: 65N30 65N38 65N50 65N15 × Cite Format Result Cite Review PDF Full Text: DOI
Janon, Alexandre; Nodet, Maëlle; Prieur, Christophe; Prieur, Clémentine Goal-oriented error estimation for parameter-dependent nonlinear problems. (English) Zbl 1401.49040 ESAIM, Math. Model. Numer. Anal. 52, No. 2, 705-728 (2018). MSC: 49M30 49M25 62F12 65C20 82C80 35Q53 90C15 × Cite Format Result Cite Review PDF Full Text: DOI
Kergrene, Kenan; Prudhomme, Serge; Chamoin, Ludovic; Laforest, Marc A new goal-oriented formulation of the finite element method. (English) Zbl 1439.65181 Comput. Methods Appl. Mech. Eng. 327, 256-276 (2017). MSC: 65N30 × Cite Format Result Cite Review PDF Full Text: DOI HAL
Chamoin, Ludovic; Pled, Florent; Allier, Pierre-Eric; Ladevèze, Pierre A posteriori error estimation and adaptive strategy for PGD model reduction applied to parametrized linear parabolic problems. (English) Zbl 1439.65108 Comput. Methods Appl. Mech. Eng. 327, 118-146 (2017). MSC: 65M60 65M15 × Cite Format Result Cite Review PDF Full Text: DOI arXiv HAL
Abdelmalik, M. R. A.; van Brummelen, E. H. Error estimation and adaptive moment hierarchies for goal-oriented approximations of the Boltzmann equation. (English) Zbl 1439.76144 Comput. Methods Appl. Mech. Eng. 325, 219-239 (2017). MSC: 76P05 65N30 35A35 35Q20 76M10 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Guo, Mengwu; Zhong, Hongzhi Strict upper and lower bounds for quantities of interest in static response sensitivity analysis. (English) Zbl 1480.74079 Appl. Math. Modelling 49, 17-34 (2017). MSC: 74G15 65N30 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Guo, Mengwu; Zhong, Hongzhi Equivalence of two strictly bounding approaches for goal-oriented error estimation. (Chinese. English summary) Zbl 1399.65209 J. Tsinghua Univ., Sci. Technol. 57, No. 4, 362-368 (2017). MSC: 65M15 65N15 65M12 81V70 × Cite Format Result Cite Review PDF Full Text: DOI
Hoang, K. C.; Kerfriden, P.; Bordas, S. P. A. A fast, certified and “tuning free” two-field reduced basis method for the metamodelling of affinely-parametrised elasticity problems. (English) Zbl 1425.74465 Comput. Methods Appl. Mech. Eng. 298, 121-158 (2016). MSC: 74S05 65N30 65N15 74B05 × Cite Format Result Cite Review PDF Full Text: DOI
Widany, K.-U.; Mahnken, R. Dual-based adaptive FEM for inelastic problems with standard FE implementations. (English) Zbl 1352.74447 Int. J. Numer. Methods Eng. 107, No. 2, 127-154 (2016). MSC: 74S05 65M60 × Cite Format Result Cite Review PDF Full Text: DOI
Maier, Matthias; Rannacher, Rolf Duality-based adaptivity in finite element discretization of heterogeneous multiscale problems. (English) Zbl 1351.65090 J. Numer. Math. 24, No. 3, 167-187 (2016). MSC: 65N30 65N12 65N15 65N50 65N55 35J25 × Cite Format Result Cite Review PDF Full Text: DOI
Rademacher, A. NCP function-based dual weighted residual error estimators for Signorini’s problem. (English) Zbl 1381.74208 SIAM J. Sci. Comput. 38, No. 3, A1743-A1769 (2016). MSC: 74S05 65N30 35Q74 35J86 65N15 74G15 × Cite Format Result Cite Review PDF Full Text: DOI
Chung, Eric T.; Leung, Wing Tat; Pollock, Sara Goal-oriented adaptivity for GMsFEM. (English) Zbl 1342.65215 J. Comput. Appl. Math. 296, 625-637 (2016). MSC: 65N30 65N50 65N15 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Guo, Mengwu; Zhong, Hongzhi Goal-oriented error estimation for beams on elastic foundation with double shear effect. (English) Zbl 1443.74049 Appl. Math. Modelling 39, No. 16, 4699-4714 (2015). MSC: 74-10 74K10 × Cite Format Result Cite Review PDF Full Text: DOI
Wang, Li; Zhong, Hongzhi A unified approach to strict upper and lower bounds of quantities in linear elasticity based on constitutive relation error estimation. (English) Zbl 1423.74112 Comput. Methods Appl. Mech. Eng. 286, 332-353 (2015). MSC: 74B05 74G45 74S05 × Cite Format Result Cite Review PDF Full Text: DOI
Verhoosel, C. V.; van Zwieten, G. J.; van Rietbergen, B.; de Borst, R. Image-based goal-oriented adaptive isogeometric analysis with application to the micro-mechanical modeling of trabecular bone. (English) Zbl 1423.74929 Comput. Methods Appl. Mech. Eng. 284, 138-164 (2015). MSC: 74S05 65N30 65D17 65N50 74M25 92C10 × Cite Format Result Cite Review PDF Full Text: DOI Link
Rüter, Marcus; Chen, Jiun-Shyan A multi-space error estimation approach for meshfree methods. (English) Zbl 1363.65192 Brandts, J. (ed.) et al., Proceedings of the international conference ‘Applications of mathematics’, Prague, Czech Republic, November 18–21, 2015. In honor of the birthday anniversaries of Ivo Babuška (90), Milan Práger (85), and Emil Vitásek (85). Prague: Czech Academy of Sciences, Institute of Mathematics (ISBN 978-80-85823-65-3). 194-205 (2015). MSC: 65N15 65N50 46E22 35J30 65N30 × Cite Format Result Cite Review PDF Full Text: Link
Brett, Charles; Elliott, Charles M.; Hintermüller, Michael; Löbhard, Caroline Mesh adaptivity in optimal control of elliptic variational inequalities with point-tracking of the state. (English) Zbl 1320.49016 Interfaces Free Bound. 17, No. 1, 21-53 (2015). MSC: 49M25 49J40 49K20 65K15 35J86 90C33 × Cite Format Result Cite Review PDF Full Text: DOI
Cliffe, K. A.; Collis, J.; Houston, P. Goal-oriented a posteriori error estimation for the travel time functional in porous media flows. (English) Zbl 1320.76066 SIAM J. Sci. Comput. 37, No. 2, B127-B152 (2015). MSC: 76M10 76S05 65N15 65N30 65N50 × Cite Format Result Cite Review PDF Full Text: DOI Link
Bürg, Markus; Nazarov, Murtazo Goal-oriented adaptive finite element methods for elliptic problems revisited. (English) Zbl 1316.65098 J. Comput. Appl. Math. 287, 125-147 (2015). MSC: 65N30 65N12 65N15 65N50 35J05 × Cite Format Result Cite Review PDF Full Text: DOI
Rannacher, Rolf Model reduction by adaptive discretization in optimal control. (English) Zbl 1320.49017 Leugering, Günter (ed.) et al., Trends in PDE constrained optimization. Cham: Birkhäuser/Springer (ISBN 978-3-319-05082-9/hbk; 978-3-319-05083-6/ebook). ISNM. International Series of Numerical Mathematics 165, 251-284 (2014). MSC: 49M25 49J20 49M05 49M15 49M29 65K10 65M50 65M60 65N22 65N30 65N50 × Cite Format Result Cite Review PDF Full Text: DOI
Kuru, G.; Verhoosel, C. V.; van der Zee, K. G.; van Brummelen, E. H. Goal-adaptive isogeometric analysis with hierarchical splines. (English) Zbl 1296.65162 Comput. Methods Appl. Mech. Eng. 270, 270-292 (2014). MSC: 65N30 65D17 65D07 × Cite Format Result Cite Review PDF Full Text: DOI
González-Estrada, O. A.; Nadal, E.; Ródenas, J. J.; Kerfriden, P.; Bordas, S. P. A.; Fuenmayor, F. J. Mesh adaptivity driven by goal-oriented locally equilibrated superconvergent patch recovery. (English) Zbl 1398.74332 Comput. Mech. 53, No. 5, 957-976 (2014). MSC: 74S05 65N30 65N15 74R10 74B05 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Hintermüller, M.; Hoppe, R. H. W.; Löbhard, C. Dual-weighted goal-oriented adaptive finite elements for optimal control of elliptic variational inequalities. (English) Zbl 1287.49030 ESAIM, Control Optim. Calc. Var. 20, No. 2, 524-546 (2014). MSC: 49M25 49J40 65K15 90C33 × Cite Format Result Cite Review PDF Full Text: DOI
Lin, Zhi-jia; Zhuang, Zhuo Enriched goal-oriented error estimation for fracture problems solved by continuum-based shell extended finite element method. (English) Zbl 1284.74118 Appl. Math. Mech., Engl. Ed. 35, No. 1, 33-48 (2014). MSC: 74R99 74S05 65L60 × Cite Format Result Cite Review PDF Full Text: DOI
Zaccardi, C.; Chamoin, L.; Cottereau, R.; Ben Dhia, H. Error estimation and model adaptation for a stochastic-deterministic coupling method based on the Arlequin framework. (English) Zbl 1352.65635 Int. J. Numer. Methods Eng. 96, No. 2, 87-109 (2013). MSC: 65N75 35R60 60G60 60H35 65N30 × Cite Format Result Cite Review PDF Full Text: DOI Link
Ladevèze, P.; Pled, F.; Chamoin, L. New bounding techniques for goal-oriented error estimation applied to linear problems. (English) Zbl 1352.74389 Int. J. Numer. Methods Eng. 93, No. 13, 1345-1380 (2013). MSC: 74S05 65G20 65N30 74G50 × Cite Format Result Cite Review PDF Full Text: DOI arXiv HAL
Parés, Núria; Díez, Pedro; Huerta, Antonio Computable exact bounds for linear outputs from stabilized solutions of the advection-diffusion-reaction equation. (English) Zbl 1352.65533 Int. J. Numer. Methods Eng. 93, No. 5, 483-509 (2013). MSC: 65N30 65N12 × Cite Format Result Cite Review PDF Full Text: DOI Link
Giraldi, L.; Nouy, A.; Legrain, G.; Cartraud, P. Tensor-based methods for numerical homogenization from high-resolution images. (English) Zbl 1297.65138 Comput. Methods Appl. Mech. Eng. 254, 154-169 (2013). MSC: 65N21 94A08 92C55 × Cite Format Result Cite Review PDF Full Text: DOI HAL
Weiser, Martin On goal-oriented adaptivity for elliptic optimal control problems. (English) Zbl 1278.65158 Optim. Methods Softw. 28, No. 5, 969-992 (2013). MSC: 65M60 65K10 49M25 × Cite Format Result Cite Review PDF Full Text: DOI
Rüter, Marcus; Gerasimov, Tymofiy; Stein, Erwin Goal-oriented explicit residual-type error estimates in XFEM. (English) Zbl 1398.74397 Comput. Mech. 52, No. 2, 361-376 (2013). MSC: 74S05 65N30 74R10 65N15 74B05 × Cite Format Result Cite Review PDF Full Text: DOI
Rannacher, Rolf; Vexler, Boris; Wollner, Winnifried A posteriori error estimation in PDE-constrained optimization with pointwise inequality constraints. (English) Zbl 1356.49052 Leugering, Günter (ed.) et al., Constrained optimization and optimal control for partial differential equations. Basel: Birkhäuser (ISBN 978-3-0348-0132-4/hbk; 978-3-0348-0133-1/ebook). ISNM. International Series of Numerical Mathematics 160, 349-373 (2012). MSC: 49M25 65N30 65K10 90C59 × Cite Format Result Cite Review PDF Full Text: DOI
Brandenburg, Christian; Lindemann, Florian; Ulbrich, Michael; Ulbrich, Stefan Advanced numerical methods for PDE constrained optimization with application to optimal design in Navier Stokes flow. (English) Zbl 1356.49019 Leugering, Günter (ed.) et al., Constrained optimization and optimal control for partial differential equations. Basel: Birkhäuser (ISBN 978-3-0348-0132-4/hbk; 978-3-0348-0133-1/ebook). ISNM. International Series of Numerical Mathematics 160, 257-275 (2012). MSC: 49J50 49Q10 76D55 49K20 × Cite Format Result Cite Review PDF Full Text: DOI
Gallimard, Laurent Error control in FORM reliability analysis. (English. French summary) Zbl 1348.74313 Eur. J. Comput. Mech. 21, No. 3-6, 231-241 (2012). MSC: 74S05 62N05 × Cite Format Result Cite Review PDF Full Text: DOI Link
Aksoylu, Burak; Bond, Stephen D.; Cyr, Eric C.; Holst, Michael Goal-oriented adaptivity and multilevel preconditioning for the Poisson-Boltzmann equation. (English) Zbl 1263.78011 J. Sci. Comput. 52, No. 1, 202-225 (2012). Reviewer: Jong Hyuk Park (Ulsan) MSC: 78M10 35Q20 65N30 65N55 65F08 78A35 78A30 65N15 × Cite Format Result Cite Review PDF 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 × Cite Format Result Cite Review PDF Full Text: DOI Link
Dedè, L.; Santos, H. A. F. A. B-spline goal-oriented error estimators for geometrically nonlinear rods. (English) Zbl 1398.74321 Comput. Mech. 49, No. 1, 35-52 (2012). MSC: 74S05 74K10 65N30 65N15 41A15 × Cite Format Result Cite Review PDF Full Text: DOI
Gallimard, L. Error bounds for the reliability index in finite element reliability analysis. (English) Zbl 1242.74114 Int. J. Numer. Methods Eng. 87, No. 8, 781-794 (2011). MSC: 74S05 74B05 65N15 65N30 × Cite Format Result Cite Review PDF Full Text: DOI Link
Ben Dhia, H.; Chamoin, Ludovic; Oden, J. Tinsley; Prudhomme, Serge A new adaptive modeling strategy based on optimal control for atomic-to-continuum coupling simulations. (English) Zbl 1230.74220 Comput. Methods Appl. Mech. Eng. 200, No. 37-40, 2675-2696 (2011). MSC: 74S30 74A25 65N75 × Cite Format Result Cite Review PDF Full Text: DOI
Rauser, Florian; Korn, Peter; Marotzke, Jochem Predicting goal error evolution from near-initial-information: a learning algorithm. (English) Zbl 1408.76085 J. Comput. Phys. 230, No. 19, 7284-7299 (2011). MSC: 76B15 76M25 × Cite Format Result Cite Review PDF Full Text: DOI
Hartmann, Ralf; Held, Joachim; Leicht, Tobias Adjoint-based error estimation and adaptive mesh refinement for the RANS and \(k-\omega\) turbulence model equations. (English) Zbl 1343.76044 J. Comput. Phys. 230, No. 11, 4268-4284 (2011). MSC: 76M25 76F65 × Cite Format Result Cite Review PDF Full Text: DOI Link
Johansson, Håkan; Larsson, Fredrik; Runesson, Kenneth Application-specific error control for parameter identification problems. (English) Zbl 1469.74054 Int. J. Numer. Methods Biomed. Eng. 27, No. 4, 608-618 (2011). MSC: 74G75 74D99 74S99 × Cite Format Result Cite Review PDF Full Text: DOI
van der Zee, Kristoffer G.; Oden, J. Tinsley; Prudhomme, Serge; Hawkins-Daarud, Andrea Goal-oriented error estimation for Cahn–Hilliard models of binary phase transition. (English) Zbl 1428.35398 Numer. Methods Partial Differ. Equations 27, No. 1, 160-196 (2011). MSC: 35Q35 65M15 65M60 × Cite Format Result Cite Review PDF Full Text: DOI
Pannachet, T.; Díez, P.; Askes, H.; Sluys, L. J. Error assessment and mesh adaptivity for regularized continuous failure models. (English) Zbl 1227.74086 Comput. Methods Appl. Mech. Eng. 199, No. 17-20, 961-978 (2010). MSC: 74S05 74R05 × Cite Format Result Cite Review PDF Full Text: DOI Link
Fick, Peter W.; Van Brummelen, E. Harald; Van Der Zee, Kristoffer G. On the adjoint-consistent formulation of interface conditions in goal-oriented error estimation and adaptivity for fluid-structure interaction. (English) Zbl 1225.74085 Comput. Methods Appl. Mech. Eng. 199, No. 49-52, 3369-3385 (2010). MSC: 74S05 74F10 × Cite Format Result Cite Review PDF Full Text: DOI
Gonçalves, João L.; Devloo, Philippe R. B.; Gomes, Sônia M. Goal-oriented error estimation for the discontinuous Galerkin method applied to the biharmonic equation. (English) Zbl 1216.65146 Kreiss, Gunilla (ed.) et al., Numerical mathematics and advanced applications 2009. Proceedings of ENUMATH 2009, the 8th European conference on numerical mathematics and advanced applications, Uppsala, Sweden, June 29–July 3, 2009. Berlin: Springer (ISBN 978-3-642-11794-7/hbk; 978-3-642-11795-4/ebook). 369-376 (2010). MSC: 65N15 65N30 35J40 × Cite Format Result Cite Review PDF Full Text: DOI
van der Zee, K. G.; van Brummelen, E. H.; De Borst, R. Goal-oriented error estimation and adaptivity for free-boundary problems: the shape-linearization approach. (English) Zbl 1209.35159 SIAM J. Sci. Comput. 32, No. 2, 1093-1118 (2010). MSC: 35R35 49M29 54C56 58C20 65N15 65N50 × Cite Format Result Cite Review PDF Full Text: DOI Link
van der Zee, K. G.; van Brummelen, E. H.; De Borst, R. Goal-oriented error estimation and adaptivity for free-boundary problems: the domain-map linearization approach. (English) Zbl 1210.35300 SIAM J. Sci. Comput. 32, No. 2, 1064-1092 (2010). MSC: 35R35 49M29 65N15 65N50 × Cite Format Result Cite Review PDF Full Text: DOI Link
Ladevèze, P.; Chamoin, L. Calculation of strict error bounds for finite element approximations of nonlinear pointwise quantities of interest. (English) Zbl 1202.74175 Int. J. Numer. Methods Eng. 84, No. 13, 1638-1664 (2010). MSC: 74S05 74R10 65N15 65N30 × Cite Format Result Cite Review PDF Full Text: DOI
Panetier, J.; Ladevèze, P.; Chamoin, L. Strict and effective bounds in goal-oriented error estimation applied to fracture mechanics problems solved with XFEM. (English) Zbl 1183.74303 Int. J. Numer. Methods Eng. 81, No. 6, 671-700 (2010). MSC: 74S05 74R10 × Cite Format Result Cite Review PDF Full Text: DOI
Prudhomme, Serge; Chamoin, Ludovic; Ben Dhia, Hachmi; Bauman, Paul T. An adaptive strategy for the control of modeling error in two-dimensional atomic-to-continuum coupling simulations. (English) Zbl 1227.74089 Comput. Methods Appl. Mech. Eng. 198, No. 21-26, 1887-1901 (2009). MSC: 74S05 74A25 65N15 × Cite Format Result Cite Review PDF Full Text: DOI
Steffens, Lindaura Maria; Díez, Pedro A simple strategy to assess the error in the numerical wave number of the finite element solution of the Helmholtz equation. (English) Zbl 1227.76041 Comput. Methods Appl. Mech. Eng. 198, No. 15-16, 1389-1400 (2009). MSC: 76M10 76Q05 × Cite Format Result Cite Review PDF Full Text: DOI Link
Parés, Núria; Díez, Pedro; Huerta, Antonio Exact bounds for linear outputs of the advection-diffusion-reaction equation using flux-free error estimates. (English) Zbl 1195.65157 SIAM J. Sci. Comput. 31, No. 4, 3064-3089 (2009). MSC: 65N15 65N30 35J25 × Cite Format Result Cite Review PDF Full Text: DOI Link
Gallimard, L. A constitutive relation error estimator based on traction-free recovery of the equilibrated stress. (English) Zbl 1183.74274 Int. J. Numer. Methods Eng. 78, No. 4, 460-482 (2009). MSC: 74S05 74B05 × Cite Format Result Cite Review PDF Full Text: DOI Link
Vidal, Yolanda; Parés, Núria; Díez, Pedro; Huerta, Antonio Bounds for quantities of interest and adaptivity in the element-free Galerkin method. (English) Zbl 1195.65175 Int. J. Numer. Methods Eng. 76, No. 11, 1782-1818 (2008). MSC: 65N30 65N15 76M25 76R99 × Cite Format Result Cite Review PDF Full Text: DOI Link
Parés, Núria; Díez, Pedro; Huerta, Antonio Bounds of functional outputs for parabolic problems. II: Bounds of the exact solution. (English) Zbl 1194.65110 Comput. Methods Appl. Mech. Eng. 197, No. 19-20, 1661-1679 (2008). MSC: 65M15 × Cite Format Result Cite Review PDF Full Text: DOI Link
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 × Cite Format Result Cite Review PDF Full Text: DOI Link
Chamoin, Ludovic; Ladevèze, Pierre A non-intrusive method for the calculation of strict and efficient bounds of calculated outputs of interest in linear viscoelasticity problems. (English) Zbl 1169.74357 Comput. Methods Appl. Mech. Eng. 197, No. 9-12, 994-1014 (2008). MSC: 74D05 74S05 × Cite Format Result Cite Review PDF Full Text: DOI
Arndt, Marcel; Luskin, Mitchell Error estimation and atomistic-continuum adaptivity for the quasicontinuum approximation of a Frenkel-Kontorova model. (English) Zbl 1160.82313 Multiscale Model. Simul. 7, No. 1, 147-170 (2008). MSC: 82B20 82D35 82C80 65Z05 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Parés, Núria; Díez, Pedro; Huerta, Antonio Exact bounds for linear outputs of the convection-diffusion-reaction equation using flux-free error estimates. (English) Zbl 1158.65344 Griebel, Michael (ed.) et al., Meshfree methods for partial differential equations IV. Papers based on the presentations at the 4th international workshop, Bonn, Germany, September 17–20, 2007. Berlin: Springer (ISBN 978-3-540-79993-1/pbk). Lecture Notes in Computational Science and Engineering 65, 215-230 (2008). MSC: 65N15 65N30 × Cite Format Result Cite Review PDF Full Text: DOI
Stein, Erwin; Rüter, Marcus; Ohnimus, Stephan Error-controlled adaptive goal-oriented modeling and finite element approximations in elasticity. (English) Zbl 1173.74443 Comput. Methods Appl. Mech. Eng. 196, No. 37-40, 3598-3613 (2007). MSC: 74S05 74B05 74B20 × Cite Format Result Cite Review PDF 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 × Cite Format Result Cite Review PDF Full Text: DOI
Oden, J. T.; Diller, K. R.; Bajaj, C.; Browne, J. C.; Hazle, J.; Babuška, I.; Bass, J.; Biduat, L.; Demkowicz, L.; Elliott, A.; Feng, Y.; Fuentes, D.; Prudhomme, S.; Rylander, M. N.; Stafford, R. J.; Zhang, Y. Dynamic data-driven finite element models for laser treatment of cancer. (English) Zbl 1114.92043 Numer. Methods Partial Differ. Equations 23, No. 4, 904-922 (2007). MSC: 92C50 92C55 49N90 65N30 × Cite Format Result Cite Review PDF Full Text: DOI
Gallimard, L.; Panetier, J. Error estimation of stress intensity factors for mixed-mode cracks. (English) Zbl 1127.74043 Int. J. Numer. Methods Eng. 68, No. 3, 299-316 (2006). MSC: 74S05 74G70 74R10 74B05 × Cite Format Result Cite Review PDF Full Text: DOI HAL
Sudarshan, R.; Amaratunga, K.; Grätsch, T. A combined approach for goal-oriented error estimation and adaptivity using operator-customized finite element wavelets. (English) Zbl 1110.74857 Int. J. Numer. Methods Eng. 66, No. 6, 1002-1035 (2006). MSC: 74S05 74K20 65T60 × Cite Format Result Cite Review PDF Full Text: DOI
Korotov, S. A posteriori error estimation of goal-oriented quantities for elliptic type BVPs. (English) Zbl 1089.65120 J. Comput. Appl. Math. 191, No. 2, 216-227 (2006). MSC: 65N15 65N30 35J25 35J40 × Cite Format Result Cite Review PDF Full Text: DOI
Parés, Núria; Díez, Pedro; Huerta, Antonio Subdomain-based flux-free a posteriori error estimators. (English) Zbl 1193.65191 Comput. Methods Appl. Mech. Eng. 195, No. 4-6, 297-323 (2006). MSC: 65N15 65N30 × Cite Format Result Cite Review PDF Full Text: DOI Link
Grätsch, Thomas; Bathe, Klaus-Jürgen Influence functions and goal-oriented error estimation for finite element analysis of shell structures. (English) Zbl 1122.74507 Int. J. Numer. Methods Eng. 63, No. 5, 709-736 (2005). MSC: 74S05 74K25 × Cite Format Result Cite Review PDF Full Text: DOI
Zdunek, A.; Rachowicz, W. A goal-oriented \(hp\)-adaptive finite element approach to radar scattering problems. (English) Zbl 1063.78024 Comput. Methods Appl. Mech. Eng. 194, No. 2-5, 657-674 (2005). MSC: 78M10 78A25 78A45 78A60 × Cite Format Result Cite Review PDF Full Text: DOI
Stein, Erwin; Rüter, Marcus; Ohnimus, Stephan Adaptive finite element analysis and modelling of solids and structures. findings, problems and trends. (English) Zbl 1060.74642 Int. J. Numer. Methods Eng. 60, No. 1, 103-138 (2004). MSC: 74S05 65N50 × Cite Format Result Cite Review PDF Full Text: DOI
Prudhomme, Serge; Oden, J. Tinsley Goal-oriented error estimation for problems in mechanics. (Estimation des erreurs de discrétisation pour des problèmes de mécanique.) (French) Zbl 1171.74448 Rev. Eur. Élém. Finis 12, No. 6, 665-689 (2003). MSC: 74S05 74B05 74H45 × Cite Format Result Cite Review PDF Full Text: DOI
Oden, J. Tinsley; Prudhomme, Serge; Westermann, Tim; Bass, Jon; Botkin, Mark E. Error estimation of eigenfrequencies for elasticity and shell problems. (English) Zbl 1058.74081 Math. Models Methods Appl. Sci. 13, No. 3, 323-344 (2003). MSC: 74S05 74H45 74K25 74B05 65M15 65N15 74G15 × Cite Format Result Cite Review PDF Full Text: DOI
Ingelström, P.; Bondeson, A. Goal-oriented error estimation and \(h\)-adaptivity for Maxwell’s equations. (English) Zbl 1054.78026 Comput. Methods Appl. Mech. Eng. 192, No. 22-24, 2597-2616 (2003). Reviewer: Ulrich Langer (Linz) MSC: 78M10 78A50 78A25 65N30 65N15 × Cite Format Result Cite Review PDF Full Text: DOI
Prudhomme, Serge; Oden, J. Tinsley; Westermann, Tim; Bass, Jon; Botkin, Mark E. Practical methods for a posteriori error estimation in engineering applications. (English) Zbl 1038.74045 Int. J. Numer. Methods Eng. 56, No. 8, 1193-1224 (2003). MSC: 74S05 74B05 65N15 × Cite Format Result Cite Review PDF Full Text: DOI
Oden, J. Tinsley; Prudhomme, Serge Estimation of modeling error in computational mechanics. (English) Zbl 1053.74049 J. Comput. Phys. 182, No. 2, 496-515 (2002). MSC: 74S05 76M10 65N15 × Cite Format Result Cite Review PDF Full Text: DOI Link