메뉴 건너뛰기




Volumn 21, Issue 7, 2011, Pages 1415-1442

Reduced basis approximation and a posteriori error estimation for the parametrized unsteady boussinesq equations

Author keywords

a posteriori error estimation; Boussinesq equations; error bounds; offline online procedure; POD Greedy sampling; real time computation; reduced basis approximation; reduced order model; stability; successive constraint method

Indexed keywords

BOUSSINESQ EQUATIONS; CONSTRAINT METHODS; ERROR BOUNDS; OFFLINE-ONLINE PROCEDURE; POD-GREEDY SAMPLING; POSTERIORI ERROR ESTIMATION; REAL-TIME COMPUTATIONS; REDUCED ORDER MODELS; REDUCED-BASIS APPROXIMATION;

EID: 79960573260     PISSN: 02182025     EISSN: None     Source Type: Journal    
DOI: 10.1142/S0218202511005441     Document Type: Article
Times cited : (55)

References (57)
  • 1
    • 0017970146 scopus 로고
    • Automatic choice of global shape functions in structural analysis
    • B. O. Almroth, P. Stern and F. A. Brogan, Automatic choice of global shape functions in structural analysis, AIAA J. 16 (1978) 525-528. (Pubitemid 8606771)
    • (1978) AIAA Journal , vol.16 , Issue.5 , pp. 525-528
    • Almroth, B.O.1    Stern, P.2    Brogan, F.A.3
  • 2
    • 77957173096 scopus 로고    scopus 로고
    • Towards real-time CFD-based aeroelastic computations using a database of reduced-order models
    • D. Amsallem, J. Cortial and C. Farhat, Towards real-time CFD-based aeroelastic computations using a database of reduced-order models, AIAA J. 48 (2010) 2029-2037.
    • (2010) AIAA J. , vol.48 , pp. 2029-2037
    • Amsallem, D.1    Cortial, J.2    Farhat, C.3
  • 3
    • 47749108243 scopus 로고    scopus 로고
    • Interpolation method for adapting reduced-order models and application to aeroelasticity
    • D. Amsallem and C. Farhat, Interpolation method for adapting reduced-order models and application to aeroelasticity, AIAA J. 46 (2008) 1803-1813.
    • (2008) AIAA J. , vol.46 , pp. 1803-1813
    • Amsallem, D.1    Farhat, C.2
  • 4
    • 0034176459 scopus 로고    scopus 로고
    • Natural convection in an anulus between two isothermal square ducts
    • H. Asan, Natural convection in an anulus between two isothermal square ducts, Int. Comm. Heat Mass Transfer 27 (2000) 367-376.
    • (2000) Int. Comm. Heat Mass Transfer , vol.27 , pp. 367-376
    • Asan, H.1
  • 5
    • 67349164332 scopus 로고    scopus 로고
    • Preconditioning constrained eigenvalue problems
    • C. G. Baker and R. B. Lehoucq, Preconditioning constrained eigenvalue problems, Linear Algebra Appl. 431 (2009) 396-408.
    • (2009) Linear Algebra Appl. , vol.431 , pp. 396-408
    • Baker, C.G.1    Lehoucq, R.B.2
  • 6
    • 15744385841 scopus 로고    scopus 로고
    • Une méthode d'«intepolation empirique»: Application à la discrétisation efficace par base réduite d'equations aux dériveés partielles
    • DOI 10.1016/j.crma.2004.08.006, PII S1631073X04004248
    • M. Barrault, Y. Maday, N. C. Nguyen and A. T. Patera, An "empirical interpolation" method: Application to effcient reduced-basis discretization of partial differential equations, C. R. Acad. Sci. Paris, Série I 339 (2004) 667-672. (Pubitemid 41447538)
    • (2004) Comptes Rendus Mathematique , vol.339 , Issue.9 , pp. 667-672
    • Barrault, M.1    Maday, Y.2    Nguyen, N.C.3    Patera, A.T.4
  • 9
    • 77950847573 scopus 로고    scopus 로고
    • A posteriori error analysis of the reduced basis method for nonaffne parametrized nonlinear PDEs
    • C. Canuto, T. Tonn and K. Urban, A posteriori error analysis of the reduced basis method for nonaffne parametrized nonlinear PDEs, SIAM J. Numer. Anal. 47 (2009) 2001-2022.
    • (2009) SIAM J. Numer. Anal. , vol.47 , pp. 2001-2022
    • Canuto, C.1    Tonn, T.2    Urban, K.3
  • 10
    • 0033295675 scopus 로고    scopus 로고
    • Evaluation of POD-based decomposition techniques applied to parameter-dependent non-turbulent flows
    • E. A. Christensen, M. Brons and J. N. Sørensen, Evaluation of POD-based decomposition techniques applied to parameter-dependent non-turbulent flows, SIAM J. Sci. Comput. 21 (2000) 1419-1434.
    • (2000) SIAM J. Sci Comput. , vol.21 , pp. 1419-1434
    • Christensen, E.A.1    Brons, M.2    Sørensen, J.N.3
  • 13
    • 0026067446 scopus 로고
    • Low-dimensional models for complex geometry flows: Application to grooved channels and circular cylinders
    • A. E. Deane, I. G. Kevrekidis, G. E. Karniadakis and S. A. Orszag, Low-dimensional models for complex geometry flows: Application to grooved channels and circular cylinders, Phys. Fluids 10 (1991) 2337-2354.
    • (1991) Phys. Fluids , vol.10 , pp. 2337-2354
    • Deane, A.E.1    Kevrekidis, I.G.2    Karniadakis, G.E.3    Orszag, S.A.4
  • 14
    • 55349102713 scopus 로고    scopus 로고
    • Reduced basis error bound computation of parameter-dependent navier-stokes equations by the natural norm approach
    • S. Deparis, Reduced basis error bound computation of parameter-dependent Navier-Stokes equations by the natural norm approach, SIAM J. Numer. Anal. 46 (2008) 2039-2067.
    • (2008) SIAM J. Numer. Anal. , vol.46 , pp. 2039-2067
    • Deparis, S.1
  • 16
    • 79960848755 scopus 로고    scopus 로고
    • An hp certified reduced basis method for parametrized time-dependent partial differential equations
    • accepted
    • J. L. Eftang, D. J. Knezevic, A. T. Patera and E. M. Rønquist, An hp certified reduced basis method for parametrized time-dependent partial differential equations, accepted 2010 Math. Comput. Model. Dynam. Syst.
    • (2010) Math. Comput. Model. Dynam. Syst
    • Eftang, J.L.1    Knezevic, D.J.2    Patera, A.T.3    Rønquist, E.M.4
  • 17
    • 78651554414 scopus 로고    scopus 로고
    • An hp certified reduced basis method for parametrized parabolic partial differential equations
    • J. L. Eftang, A. T. Patera and E. M. Rønquist, An hp certified reduced basis method for parametrized parabolic partial differential equations, SIAM J. Sci. Comput. 32 (2010) 3170-3200.
    • (2010) SIAM J. Sci Comput. , vol.32 , pp. 3170-3200
    • Eftang, J.L.1    Patera, A.T.2    Rønquist, E.M.3
  • 18
    • 0020547404 scopus 로고
    • On the error behavior of the reduced basis technique for nonlinear finite element approximations
    • J. P. Fink and W. C. Rheinboldt, On the error behavior of the reduced basis technique for nonlinear finite element approximations, Z. Angew. Math. Mech. 63 (1983) 21-28. (Pubitemid 13507890)
    • (1983) Zeitschrift fur angewandte Mathematik und Mechanik , vol.63 , Issue.1 , pp. 21-28
    • Fink, J.P.1    Rheinboldt, W.C.2
  • 19
    • 0032648581 scopus 로고    scopus 로고
    • Stability of multiple steady states of convection in laterally heated cavities
    • A. Yu. Gelfgat, P. Z. Bar-Yoseph and A. L. Yarin, Stability of multiple steady states of convection in laterally heated cavities, J. Fluid Mech. 388 (1999) 315-334.
    • (1999) J Fluid Mech. , vol.388 , pp. 315-334
    • Yu. Gelfgat, A.1    Bar-Yoseph, P.Z.2    Yarin, A.L.3
  • 21
    • 34547943108 scopus 로고    scopus 로고
    • Effcient reduced-basis treatment of nonaffne and nonlinear partial differential equations
    • M. A. Grepl, Y. Maday, N. C. Nguyen and A. T. Patera, Effcient reduced-basis treatment of nonaffne and nonlinear partial differential equations, M2AN Math. Model. Numer. Anal. 41 (2007) 575-605.
    • (2007) M2AN Math. Model. Numer. Anal. , vol.41 , pp. 575-605
    • Grepl, M.A.1    Maday, Y.2    Nguyen, N.C.3    Patera, A.T.4
  • 22
    • 15744385753 scopus 로고    scopus 로고
    • A posteriori error bounds for reduced-basis approximations of parametrized parabolic partial differential equations
    • DOI 10.1051/m2an:2005006
    • M. A. Grepl and A. T. Patera, A posteriori error bounds for reduced-basis approximations of parametrized parabolic partial differential equations, M2AN Math. Model. Numer. Anal. 39 (2005) 157-181. (Pubitemid 40419347)
    • (2005) Mathematical Modelling and Numerical Analysis , vol.39 , Issue.1 , pp. 157-181
    • Grepl, M.A.1    Patera, A.T.2
  • 24
    • 33750482967 scopus 로고    scopus 로고
    • Reduced-order modeling of time-dependent PDEs with multiple parameters in the boundary data
    • DOI 10.1016/j.cma.2006.08.004, PII S0045782506002337
    • M. D. Gunzburger, J. Peterson and J. N. Shadid, Reduced-order modeling of time-dependent PDEs with multiple parameters in the boundary data, Comput. Methods Appl. Mech. 196 (2007) 1030-1047. (Pubitemid 44644875)
    • (2007) Computer Methods in Applied Mechanics and Engineering , vol.196 , Issue.4-6 , pp. 1030-1047
    • Gunzburger, M.D.1    Peterson, J.S.2    Shadid, J.N.3
  • 26
    • 41549118036 scopus 로고    scopus 로고
    • Reduced basis method for finite volume approximations of parametrized evolution equations
    • B. Haasdonk and M. Ohlberger, Reduced basis method for finite volume approximations of parametrized evolution equations, M2AN Math. Model. Numer. Anal. 42 (2008) 277-302.
    • (2008) M2AN Math. Model. Numer. Anal. , vol.42 , pp. 277-302
    • Haasdonk, B.1    Ohlberger, M.2
  • 27
    • 33750977082 scopus 로고    scopus 로고
    • Proper orthogonal decomposition surrogate models for nonlinear dynamical systems: Error estimates and suboptimal control
    • Springer
    • M. Hinze and S. Volkwein, Proper orthogonal decomposition surrogate models for nonlinear dynamical systems: Error estimates and suboptimal control, in Lecture Notes in Computational Science and Engineering, Vol. 45 (Springer, 2005).
    • (2005) Lecture Notes in Computational Science and Engineering , vol.45
    • Hinze, M.1    Volkwein, S.2
  • 29
    • 36148955493 scopus 로고    scopus 로고
    • A successive constraint linear optimization method for lower bounds of parametric coercivity and inf-sup stability constants
    • D. B. P. Huynh, G. Rozza, S. Sen and A. T. Patera, A successive constraint linear optimization method for lower bounds of parametric coercivity and inf-sup stability constants, C. R. Acad. Sci. Paris, Série I 345 (2007) 473-478.
    • (2007) C. R. Acad. Sci. Paris, Série I , vol.345 , pp. 473-478
    • Huynh, D.B.P.1    Rozza, G.2    Sen, S.3    Patera, A.T.4
  • 30
    • 0024680166 scopus 로고
    • Numerical solutions for transient natural convection in a square cavity with different sidewall temperatures
    • J. M. Hyun and J. W. Lee, Numerical solutions for transient natural convection in a square cavity with different sidewall temperatures, Int. J. Heat Fluid Flow 10 (1989) 146-151.
    • (1989) Int J. Heat Fluid Flow , vol.10 , pp. 146-151
    • Hyun, J.M.1    Lee, J.W.2
  • 31
    • 0004159331 scopus 로고    scopus 로고
    • A reduced basis method for control problems governed by PDEs
    • eds. W. Desch, F. Kappel and K. Kunisch (Birkhäuser)
    • K. Ito and S. S. Ravindran, A reduced basis method for control problems governed by PDEs, in Control and Estimation of Distributed Parameter Systems, eds. W. Desch, F. Kappel and K. Kunisch (Birkhäuser, 1998), pp. 153-168.
    • (1998) Control and Estimation of Distributed Parameter Systems , pp. 153-168
    • Ito, K.1    Ravindran, S.S.2
  • 32
    • 0000104411 scopus 로고    scopus 로고
    • A reduced-order method for simulation and control of fluid flows
    • DOI 10.1006/jcph.1998.5943, PII S0021999198959435
    • K. Ito and S. S. Ravindran, A reduced-order method for simulation and control of fluid flows, J. Comput. Phys. 143 (1998) 403-425. (Pubitemid 128345940)
    • (1998) Journal of Computational Physics , vol.143 , Issue.2 , pp. 403-425
    • Ito, K.1    Ravindran, S.S.2
  • 34
    • 0035176135 scopus 로고    scopus 로고
    • Reduced order feedback synthesis for viscous incompressible flows
    • DOI 10.1016/S0895-7177(00)00237-5, PII S0895717700002375
    • K. Ito and J. D. Schroeter, Reduced order feedback synthesis for viscous incompressible flows, Math. Comput. Model. 33 (2001) 173-192. (Pubitemid 32062562)
    • (2001) Mathematical and Computer Modelling , vol.33 , Issue.1-3 , pp. 173-192
    • Ito, K.1    Schroeter, J.D.2
  • 35
    • 26844562908 scopus 로고    scopus 로고
    • Reduced-basis modeling of turbulent plane channel flow
    • DOI 10.1016/j.compfluid.2004.11.005, PII S0045793005000101
    • P. S. Johansson, H. I. Andersson and E. M. Rønquist, Reduced-basis modeling of turbulent plane channel flow, Comput. & Fluids 35 (2006) 189-207. (Pubitemid 41448095)
    • (2006) Computers and Fluids , vol.35 , Issue.2 , pp. 189-207
    • Johansson, P.S.1    Andersson, H.I.2    Ronquist, E.M.3
  • 36
    • 0001255117 scopus 로고
    • Numerical and hydrodynamic stability: Towards error control in computational fluid dynamics
    • C. Johnson, R. Rannacher and M. Boman, Numerical and hydrodynamic stability: Towards error control in computational fluid dynamics, SIAM J. Numer. Anal. 32 (1995) 1058-1079.
    • (1995) SIAM J. Numer. Anal. , vol.32 , pp. 1058-1079
    • Johnson, C.1    Rannacher, R.2    Boman, M.3
  • 37
  • 38
    • 39749193516 scopus 로고    scopus 로고
    • A numerical study of natural convection in a square enclosure with a circular cylinder at different vertical locations
    • DOI 10.1016/j.ijheatmasstransfer.2007.06.033, PII S0017931007004577
    • B. S. Kim, D. S. Lee, M. Y. Ha and H. S. Yoon, A numerical study of natural convection in a square enclosure with a circular cylinder at different vertical locations, Int. J. Heat Mass Transfer 51 (2008) 1888-1906. (Pubitemid 351308016)
    • (2008) International Journal of Heat and Mass Transfer , vol.51 , Issue.7-8 , pp. 1888-1906
    • Kim, B.S.1    Lee, D.S.2    Ha, M.Y.3    Yoon, H.S.4
  • 39
    • 43149123393 scopus 로고    scopus 로고
    • LibMesh: A C++ library for parallel adaptive mesh refinement/coarsening simulations
    • B. S. Kirk, J. W. Peterson, R. M. Stogner and G. F. Carey, libMesh: A C++ library for parallel adaptive mesh refinement/coarsening simulations, Engrg. Comput. 23 (2006) 237-254.
    • (2006) Engrg Comput. , vol.23 , pp. 237-254
    • Kirk, B.S.1    Peterson, J.W.2    Stogner, R.M.3    Carey, G.F.4
  • 40
    • 77950795079 scopus 로고    scopus 로고
    • A certified reduced basis method for the Fokker-Planck equation of dilute polymeric fluids: FENE dumbbells in extensional flow
    • D. J. Knezevic and A. T. Patera, A certified reduced basis method for the Fokker-Planck equation of dilute polymeric fluids: FENE dumbbells in extensional flow, SIAM J. Sci. Comput. 32 (2010) 793-817.
    • (2010) SIAM J. Sci Comput. , vol.32 , pp. 793-817
    • Knezevic, D.J.1    Patera, A.T.2
  • 41
    • 78951483251 scopus 로고    scopus 로고
    • A high-performance parallel implementation of the certified reduced basis method
    • D. J. Knezevic and J. W. Peterson, A high-performance parallel implementation of the certified reduced basis method, Comput. Methods Appl. Mech. Engrg. 200 (2011) 1455-1466.
    • (2011) Comput. Methods Appl. Mech. Engrg. , vol.200 , pp. 1455-1466
    • Knezevic, D.J.1    Peterson, J.W.2
  • 43
    • 79960847705 scopus 로고    scopus 로고
    • private communication
    • Y. Maday, private communication.
    • Maday, Y.1
  • 44
    • 70349560243 scopus 로고    scopus 로고
    • Reduced basis approximation and a posteriori error estimation for the time-dependent viscous burgers equation
    • N. C. Nguyen, G. Rozza and A. T. Patera, Reduced basis approximation and a posteriori error estimation for the time-dependent viscous Burgers equation, Calcolo 46 (2009) 157-185.
    • (2009) Calcolo , vol.46 , pp. 157-185
    • Nguyen, N.C.1    Rozza, G.2    Patera, A.T.3
  • 45
    • 15744376916 scopus 로고    scopus 로고
    • Certified real-time solution of parametrized partial differential equations
    • ed., S. Yip Springer
    • N. C. Nguyen, K. Veroy and A. T. Patera, Certified real-time solution of parametrized partial differential equations, in Handbook of Materials Modeling, ed. S. Yip (Springer, 2005), pp. 1523-1558.
    • (2005) Handbook of Materials Modeling , pp. 1523-1558
    • Nguyen, N.C.1    Veroy, K.2    Patera, A.T.3
  • 46
    • 0019009732 scopus 로고
    • Reduced basis technique for nonlinear analysis of structures
    • A. K. Noor and J. M. Peters, Reduced basis technique for nonlinear analysis of structures, AIAA J. 18 (1980) 455-462.
    • (1980) AIAA J. , vol.18 , pp. 455-462
    • Noor, A.K.1    Peters, J.M.2
  • 47
    • 84966262223 scopus 로고
    • Estimation of the error in the reduced basis method solution of nonlinear equations
    • T. A. Porsching, Estimation of the error in the reduced basis method solution of nonlinear equations, Math. Comput. 45 (1985) 487-496.
    • (1985) Math. Comput. , vol.45 , pp. 487-496
    • Porsching, T.A.1
  • 48
    • 0023577190 scopus 로고
    • The reduced-basis method for initial value problems
    • T. A. Porsching and M. Y. Lin Lee, The reduced-basis method for initial value problems, SIAM J. Numer. Anal. 24 (1987) 1277-1287. (Pubitemid 18531142)
    • (1987) SIAM Journal on Numerical Analysis , vol.24 , Issue.6 , pp. 1277-1287
    • Porsching, T.A.1    Lee, M.L.2
  • 50
    • 34547264298 scopus 로고    scopus 로고
    • Numerical solution of parametrized Navier-Stokes equations by reduced basis methods
    • DOI 10.1002/num.20249
    • A. Quarteroni and G. Rozza, Numerical solution of parametrized Navier-Stokes equations by reduced basis method, Numer. Methods Partial Differential Equations 23 (2007) 923-948. (Pubitemid 47128295)
    • (2007) Numerical Methods for Partial Differential Equations , vol.23 , Issue.4 , pp. 923-948
    • Quarteronl, A.1    Rozza, G.2
  • 52
    • 33745908236 scopus 로고    scopus 로고
    • Reduced-basis output bound methods for parabolic problems
    • DOI 10.1093/imanum/dri044
    • D. Rovas, L. Machiels and Y. Maday, Reduced basis output bounds methods for parabolic problems, IMA J. Numer. Anal. 26 (2006) 423-445. (Pubitemid 44048220)
    • (2006) IMA Journal of Numerical Analysis , vol.26 , Issue.3 , pp. 423-445
    • Rovas, D.V.1    Machiels, L.2    Maday, Y.3
  • 53
    • 53749107686 scopus 로고    scopus 로고
    • Reduced basis approximation and a posteriori error estimation for affnely parametrized elliptic coercive partial differential equations: Application to transport and continuum mechanics
    • G. Rozza, D. B. P. Huynh and A. T. Patera, Reduced basis approximation and a posteriori error estimation for affnely parametrized elliptic coercive partial differential equations: Application to transport and continuum mechanics, Archives Comput. Methods Engrg. 15 (2008) 229-275.
    • (2008) Archives Comput Methods Engrg. , vol.15 , pp. 229-275
    • Rozza, G.1    Huynh, D.B.P.2    Patera, A.T.3
  • 54
    • 15744406041 scopus 로고    scopus 로고
    • Certified real-time solution of the parametrized steady incompressible Navier-Stokes equations: Rigorous reduced-basis a posteriori error bounds
    • DOI 10.1002/fld.867, 8th Conference on Numerical Methods for Fluid Dynamics: Part 1
    • K. Veroy and A. T. Patera, Certified real-time solution of the parametrized steady incompressible Navier-Stokes equations; rigorous reduced-basis a posteriori error bounds, Int. J. Numer. Methods Fluids 47 (2005) 773-788. (Pubitemid 40413113)
    • (2005) International Journal for Numerical Methods in Fluids , vol.47 , Issue.8-9 , pp. 773-788
    • Veroy, K.1    Patera, A.T.2
  • 55
    • 0345017124 scopus 로고    scopus 로고
    • Approximation par base réduite de l'équation de Burgers visqueuse: Bornes d'erreur a posteriori rigoureuses
    • DOI 10.1016/j.crma.2003.09.023
    • K. Veroy, C. Prud'homme and A. T. Patera, Reduced-basis approximation of the viscous Burgers equation: Rigorous a posteriori error bounds, C. R. Acad. Sci. Paris, Série I 337 (2003) 619-624. (Pubitemid 37445662)
    • (2003) Comptes Rendus Mathematique , vol.337 , Issue.9 , pp. 619-624
    • Veroy, K.1    Prud'homme, C.2    Patera, A.T.3
  • 56
    • 85088184409 scopus 로고    scopus 로고
    • A posteriori error bounds for reduced-basis approximation of parametrized noncoercive and nonlinear elliptic partial differential equations
    • K. Veroy, C. Prud'homme, D. V. Rovas and A. T. Patera, A posteriori error bounds for reduced-basis approximation of parametrized noncoercive and nonlinear elliptic partial differential equations, in Proc. 16th AIAA Computational Fluid Dynamics Conf., Paper 2003-3847, 2003.
    • (2003) Proc. 16th AIAA Computational Fluid Dynamics Conf. Paper , pp. 2003-3847
    • Veroy, K.1    Prud'homme, C.2    Rovas, D.V.3    Patera, A.T.4
  • 57
    • 33144478120 scopus 로고    scopus 로고
    • Flow visualization of natural convection in a tall, air-filled vertical cavity
    • DOI 10.1016/j.ijheatmasstransfer.2005.06.045, PII S0017931005005922
    • J. L. Wright, H. Jin, K. G. T. Hollands and D. Naylor, Flow visualization of natural convection in a tall, air-filled vertical cavity, Int. J. Heat Mass Transfer 49 (2006) 889-904. (Pubitemid 43267702)
    • (2006) International Journal of Heat and Mass Transfer , vol.49 , Issue.5-6 , pp. 889-904
    • Wright, J.L.1    Jin, H.2    Hollands, K.G.T.3    Naylor, D.4


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.