TY - STD TI - Lorenz B, Biros G, Ghattas O, Heinkenschloss M, Keyes D, Mallick B, Tenorio L, van Bloemen Waanders B, Willcox K, Marzouk Y, editors. Large-scale inverse problems and quantification of uncertainty. Vol. 712. Chichester: Wiley; 2011. ID - ref1 ER - TY - STD TI - Maday Y, Ronquist EM. A reduced-basis element method. C R Acad Sci Paris Ser I. 2002;335:195–200. ID - ref2 ER - TY - JOUR AU - Kunisch, K. AU - Volkwein, S. PY - 2001 DA - 2001// TI - Galerkin proper orthogonal decomposition methods for parabolic problems JO - Numer Math VL - 148 UR - https://doi.org/10.1007/s002110100282 DO - 10.1007/s002110100282 ID - Kunisch2001 ER - TY - JOUR AU - Chinesta, F. AU - Ammar, A. AU - Cueto, E. PY - 2010 DA - 2010// TI - Recent advances and new challenges in the use of the proper generalized decomposition for solving multidimensional models JO - Arch Comput Methods Eng VL - 17 UR - https://doi.org/10.1007/s11831-010-9049-y DO - 10.1007/s11831-010-9049-y ID - Chinesta2010 ER - TY - STD TI - Chinesta F, Keunings R, Leygue A. The proper generalized decomposition for advanced numerical simulations. A primer. Springerbriefs in applied sciences and technology. Cham: Springer; 2014. ID - ref5 ER - TY - JOUR AU - Blanco, P. J. AU - Leiva, J. S. AU - Feijóo, R. A. AU - Buscaglia, G. C. PY - 2011 DA - 2011// TI - Black-box decomposition approach for computational hemodynamics: one-dimensional models JO - Comput Methods Appl Mech Eng VL - 200 UR - https://doi.org/10.1016/j.cma.2010.12.006 DO - 10.1016/j.cma.2010.12.006 ID - Blanco2011 ER - TY - STD TI - Formaggia L, Quarteroni A, Veneziani A, editors. Cardiovascular mathematics, modelling and simulation of the circulatory system. Modelling simulation and applications. Vol. 1. Milano: Springer; 2009 ID - ref7 ER - TY - JOUR AU - Bruckstein, A. M. AU - Donoho, D. L. AU - Elad, M. PY - 2009 DA - 2009// TI - From sparse solutions of systems of equations to sparse modeling of signal and images JO - SIAM Rev VL - 51 UR - https://doi.org/10.1137/060657704 DO - 10.1137/060657704 ID - Bruckstein2009 ER - TY - CHAP AU - Ern, A. AU - Perotto, S. AU - Veneziani, A. ED - Kunisch, K. ED - Of, G. ED - Steinbach, O. PY - 2008 DA - 2008// TI - Hierarchical model reduction for advection–diffusion–reaction problems BT - Numerical mathematics and advanced applications PB - Springer CY - Berlin UR - https://doi.org/10.1007/978-3-540-69777-0_84 DO - 10.1007/978-3-540-69777-0_84 ID - Ern2008 ER - TY - JOUR AU - Perotto, S. AU - Ern, A. AU - Veneziani, A. PY - 2010 DA - 2010// TI - Hierarchical local model reduction for elliptic problems: a domain decomposition approach JO - Multiscale Model Simul VL - 8 UR - https://doi.org/10.1137/090756624 DO - 10.1137/090756624 ID - Perotto2010 ER - TY - JOUR AU - Perotto, S. AU - Veneziani, A. PY - 2014 DA - 2014// TI - Coupled model and grid adaptivity in hierarchical reduction of elliptic problems JO - J Sci Comput VL - 60 UR - https://doi.org/10.1007/s10915-013-9804-y DO - 10.1007/s10915-013-9804-y ID - Perotto2014 ER - TY - CHAP AU - Perotto, S. AU - Zilio, A. ED - Cangiani, A. ED - Davidchack, R. ED - Georgoulis, E. ED - Gorban, A. ED - Levesley, J. ED - Tretyakov, M. PY - 2013 DA - 2013// TI - Hierarchical model reduction: three different approaches BT - Numerical mathematics and advanced applications PB - Springer CY - Berlin ID - Perotto2013 ER - TY - CHAP AU - Perotto, S. ED - Idelsohn, S. R. PY - 2014 DA - 2014// TI - A survey of hierarchical model (Hi-Mod) reduction methods for elliptic problems BT - Numerical simulations of coupled problems in engineering PB - Springer CY - Cham UR - https://doi.org/10.1007/978-3-319-06136-8_10 DO - 10.1007/978-3-319-06136-8_10 ID - Perotto2014 ER - TY - JOUR AU - Eriksson, K. AU - Johnson, C. AU - Thomée, V. PY - 1985 DA - 1985// TI - Time discretization of parabolic problems by the discontinuous Galerkin method JO - RAIRO Model Math Anal Numer VL - 19 ID - Eriksson1985 ER - TY - STD TI - Thomée V. Galerkin finite element methods for parabolic problems. 2nd ed. Springer series in computational mathematics. Vol. 25. Berlin: Springer; 2006 ID - ref15 ER - TY - BOOK AU - Eriksson, K. AU - Estep, D. AU - Hansbo, P. AU - Johnson, C. PY - 1996 DA - 1996// TI - Computational differential equations PB - Cambridge University Press CY - Cambridge ID - Eriksson1996 ER - TY - JOUR AU - Becker, R. AU - Rannacher, R. PY - 2001 DA - 2001// TI - An optimal control approach to a posteriori error estimation in finite element methods JO - Acta Numer VL - 10 UR - https://doi.org/10.1017/S0962492901000010 DO - 10.1017/S0962492901000010 ID - Becker2001 ER - TY - JOUR AU - Giles, M. B. AU - Süli, E. PY - 2002 DA - 2002// TI - Adjoint methods for PDEs: a posteriori error analysis and postprocessing by duality JO - Acta Numer VL - 11 UR - https://doi.org/10.1017/S096249290200003X DO - 10.1017/S096249290200003X ID - Giles2002 ER - TY - JOUR AU - Oden, J. T. AU - Prudhomme, S. PY - 2001 DA - 2001// TI - Goal-oriented error estimation and adaptivity for the finite element method JO - Comput Math Appl VL - 41 UR - https://doi.org/10.1016/S0898-1221(00)00317-5 DO - 10.1016/S0898-1221(00)00317-5 ID - Oden2001 ER - TY - JOUR AU - Braack, M. AU - Ern, A. PY - 2003 DA - 2003// TI - A posteriori control of modeling errors and discretization errors JO - Multiscale Model Simul VL - 1 UR - https://doi.org/10.1137/S1540345902410482 DO - 10.1137/S1540345902410482 ID - Braack2003 ER - TY - JOUR AU - Micheletti, S. AU - Perotto, S. AU - David, F. PY - 2013 DA - 2013// TI - Model adaptation enriched with an anisotropic mesh spacing for nonlinear equations: application to environmental and CFD problems JO - Numer Math Theor Methods Appl VL - 6 ID - Micheletti2013 ER - TY - JOUR AU - Stein, E. AU - Rüter, M. AU - Ohnimus, S. PY - 2007 DA - 2007// TI - Error-controlled adaptive goal-oriented modeling and finite element approximations in elasticity JO - Comput Methods Appl Mech Eng VL - 196 UR - https://doi.org/10.1016/j.cma.2006.10.032 DO - 10.1016/j.cma.2006.10.032 ID - Stein2007 ER - TY - JOUR AU - Verfürth, R. PY - 2003 DA - 2003// TI - A posteriori error estimate for finite element discretizations of the heat equation JO - Calcolo VL - 40 UR - https://doi.org/10.1007/s10092-003-0073-2 DO - 10.1007/s10092-003-0073-2 ID - Verfürth2003 ER - TY - JOUR AU - Cascón, J. M. AU - Ferragut, L. AU - Asensio, M. I. PY - 2006 DA - 2006// TI - Space–time adaptive algorithm for the mixed parabolic problem JO - Numer Math VL - 103 UR - https://doi.org/10.1007/s00211-006-0677-y DO - 10.1007/s00211-006-0677-y ID - Cascón2006 ER - TY - JOUR AU - Meidner, D. AU - Vexler, B. PY - 2007 DA - 2007// TI - Adaptive space–time finite element methods for parabolic optimization problems JO - SIAM J Control Optim VL - 46 UR - https://doi.org/10.1137/060648994 DO - 10.1137/060648994 ID - Meidner2007 ER - TY - JOUR AU - Micheletti, S. AU - Perotto, S. PY - 2010 DA - 2010// TI - Space–time adaptation for purely diffusive problems in an anisotropic framework JO - Int J Numer Anal Model VL - 7 ID - Micheletti2010 ER - TY - JOUR AU - Katz, G. E. AU - Berkowitz, B. AU - Guadagnini, A. AU - Saaltink, M. W. PY - 2011 DA - 2011// TI - Experimental and modeling investigation of multicomponent reactive transport in porous media JO - J Contam Hydrol VL - 120–121 UR - https://doi.org/10.1016/j.jconhyd.2009.11.002 DO - 10.1016/j.jconhyd.2009.11.002 ID - Katz2011 ER - TY - BOOK AU - Lions, J. -. L. AU - Magenes, E. PY - 1972 DA - 1972// TI - Non homogeneous boundary value problems and applications PB - Springer CY - Berlin UR - https://doi.org/10.1007/978-3-642-65161-8 DO - 10.1007/978-3-642-65161-8 ID - Lions1972 ER - TY - STD TI - Dautray R, Lions J-L. Mathematical analysis and numerical methods for science and technology: evolution problems I. Vol. 5. Berlin: Springer; 1992 ID - ref29 ER - TY - STD TI - Perotto S. Hierarchical model (Hi-Mod) reduction in non-rectilinear domains. In: Erhel J, Gander M, Halpern L, Pichot G, Sassi T, Widlund O, editors. Lect. notes comput. sci. eng. Vol. 98. Cham: Springer; 2014. p. 477–485 ID - ref30 ER - TY - STD TI - Aletti M, Perotto S, Veneziani A. Educated bases for the himod reduction of advection–diffusion–reaction problems with general boundary conditions (2015). MOX report, 37/2015. ID - ref31 ER - TY - JOUR AU - Bellhouse, B. J. AU - Bellhouse, F. H. AU - Curl, C. M. AU - MacMillan, T. I. AU - Gunning, A. J. AU - Spratt, E. H. AU - MacMurray, S. B. AU - Nelems, J. M. PY - 1973 DA - 1973// TI - A high efficiency membrane oxygenator and pulsatile pumping system and its application to animal trials JO - Trans Am. Soc. Artif Int Organs VL - 19 UR - https://doi.org/10.1097/00002480-197301900-00014 DO - 10.1097/00002480-197301900-00014 ID - Bellhouse1973 ER - TY - JOUR AU - Hecht, F. PY - 2012 DA - 2012// TI - New developements in freefem++ JO - J Numer Math VL - 20 ID - Hecht2012 ER - TY - JOUR AU - Bank, R. E. AU - Smith, R. K. PY - 1993 DA - 1993// TI - A posteriori error estimates based on hierarchical bases JO - SIAM J Numer Anal VL - 30 UR - https://doi.org/10.1137/0730048 DO - 10.1137/0730048 ID - Bank1993 ER - TY - JOUR AU - Dörfler, W. AU - Nochetto, R. H. PY - 2002 DA - 2002// TI - Small data oscillation implies the saturation assumption JO - Numer Math VL - 91 UR - https://doi.org/10.1007/s002110100321 DO - 10.1007/s002110100321 ID - Dörfler2002 ER - TY - JOUR AU - Achchab, B. AU - Achchab, S. AU - Agouzal, A. PY - 2004 DA - 2004// TI - Some remarks about the hierarchical a posteriori error estimate JO - Numer Methods Partial Differ. Equ. VL - 20 UR - https://doi.org/10.1002/num.20016 DO - 10.1002/num.20016 ID - Achchab2004 ER - TY - JOUR AU - Griewank, A. AU - Walther, A. PY - 2000 DA - 2000// TI - Algorithm 799: revolve: an implementation of checkpointing for the reverse or adjoint mode of computational differentiation JO - ACM Trans Math Softw VL - 26 UR - https://doi.org/10.1145/347837.347846 DO - 10.1145/347837.347846 ID - Griewank2000 ER - TY - JOUR AU - Clément, P. PY - 1975 DA - 1975// TI - Approximation by finite element functions using local regularization JO - RAIRO Anal Numer VL - 2 ID - Clément1975 ER - TY - JOUR AU - Ainsworth, M. PY - 1998 DA - 1998// TI - A posteriori error estimation for fully discrete hierarchic models of elliptic boundary value problems on thin domains JO - Numer Math VL - 80 UR - https://doi.org/10.1007/s002110050370 DO - 10.1007/s002110050370 ID - Ainsworth1998 ER -