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Volumn 79, Issue 10, 2009, Pages 1203-1244

Guaranteed energy error bounds for the Poisson equation using a flux-free approach: Solving the local problems in subdomains

Author keywords

Adaptivity; Error estimation; Exact guaranteed strict bounds; Flux free estimate; Partition of unity; Poisson equation; Residual based estimators; Subdomain a posteriori error estimation

Indexed keywords

ADAPTIVITY; ERROR ESTIMATION; EXACT/GUARANTEED/STRICT BOUNDS; PARTITION OF UNITY; RESIDUAL-BASED ESTIMATORS; SUBDOMAIN A POSTERIORI ERROR ESTIMATION;

EID: 69249149571     PISSN: 00295981     EISSN: 10970207     Source Type: Journal    
DOI: 10.1002/nme.2593     Document Type: Article
Times cited : (33)

References (29)
  • 1
    • 77951274033 scopus 로고    scopus 로고
    • Exact bounds for linear outputs of the advection-diffusion-reaction equation using flux-free error estimates
    • accepted for publication
    • Parés N, Díez P, Huerta A. Exact bounds for linear outputs of the advection-diffusion-reaction equation using flux-free error estimates. SIAM Journal on Scientific Computing, accepted for publication.
    • SIAM Journal on Scientific Computing
    • Parés, N.1    Díez, P.2    Huerta, A.3
  • 2
    • 0040189976 scopus 로고
    • Geradin MG (ed.), Martinus Nijhoff Publishers: The Hague, Solid Mechanics Archives, Special Memorial Vol
    • Geradin MG (ed.). B. M. Fraeijs de Veubeke Memorial Volume of Selected Papers. Martinus Nijhoff Publishers: The Hague, 1980. Solid Mechanics Archives, Special Memorial Vol.
    • (1980) B. M. Fraeijs de Veubeke Memorial Volume of Selected Papers
  • 3
    • 0021482394 scopus 로고
    • The self-equilibration of residuals and complementary a posteriori error estimates in the finite element method
    • Kelly DW. The self-equilibration of residuals and complementary a posteriori error estimates in the finite element method. International Journal for Numerical Methods in Engineering 1984; 20(8):1491-1506.
    • (1984) International Journal for Numerical Methods in Engineering , vol.20 , Issue.8 , pp. 1491-1506
    • Kelly, D.W.1
  • 4
    • 0001585002 scopus 로고
    • Error estimate procedure in the finite element method and applications
    • Ladevèze P, Leguillon D. Error estimate procedure in the finite element method and applications. SIAM Journal on Numerical Analysis 1983; 20(3):485-509.
    • (1983) SIAM Journal on Numerical Analysis , vol.20 , Issue.3 , pp. 485-509
    • Ladevèze, P.1    Leguillon, D.2
  • 6
    • 0003602782 scopus 로고    scopus 로고
    • Numerical Mathematics and Scientific Computation. The Clarendon Press, Oxford University Press: New York
    • Babuška I, Strouboulis T. The Finite Element Method and its Reliability. Numerical Mathematics and Scientific Computation. The Clarendon Press, Oxford University Press: New York, 2001.
    • (2001) The Finite Element Method and its Reliability
    • Babuška, I.1    Strouboulis, T.2
  • 7
    • 18844373516 scopus 로고    scopus 로고
    • Mechanical Engineering Series. Springer: New York, Translated from the 2001 French original by Strouboulis Theofanis
    • Ladevèze P, Pelle JP. Mastering Calculations in Linear and Nonlinear Mechanics. Mechanical Engineering Series. Springer: New York, 2005. Translated from the 2001 French original by Strouboulis Theofanis.
    • (2005) Mastering Calculations in Linear and Nonlinear Mechanics
    • Ladevèze, P.1    Pelle, J.P.2
  • 9
    • 0043048185 scopus 로고    scopus 로고
    • A posteriori error estimators related to equilibrium defaults of finite element solutions for elastostatic problems
    • Maunder EAW, Zhong HG, Beckers P. A posteriori error estimators related to equilibrium defaults of finite element solutions for elastostatic problems. Finite Elements in Analysis and Design 1997; 26(3):171-192.
    • (1997) Finite Elements in Analysis and Design , vol.26 , Issue.3 , pp. 171-192
    • Maunder, E.A.W.1    Zhong, H.G.2    Beckers, P.3
  • 11
    • 16244390315 scopus 로고    scopus 로고
    • Computing bounds for linear functionals of exact weak solutions to Poisson's equation
    • (electronic)
    • Sauer-Budge AM, Bonet J, Huerta A, Peraire J. Computing bounds for linear functionals of exact weak solutions to Poisson's equation. SIAM Journal on Numerical Analysis 2004; 42(4):1610-1630 (electronic).
    • (2004) SIAM Journal on Numerical Analysis , vol.42 , Issue.4 , pp. 1610-1630
    • Sauer-Budge, A.M.1    Bonet, J.2    Huerta, A.3    Peraire, J.4
  • 12
    • 16244368476 scopus 로고    scopus 로고
    • Computing bounds for linear functionals of exact weak solutions to the advection- diffusion-reaction equation
    • (electronic)
    • Sauer-Budge AM, Peraire J. Computing bounds for linear functionals of exact weak solutions to the advection- diffusion-reaction equation. SIAM Journal on Scientific Computing 2004; 26(2):636-652 (electronic).
    • (2004) SIAM Journal on Scientific Computing , vol.26 , Issue.2 , pp. 636-652
    • Sauer-Budge, A.M.1    Peraire, J.2
  • 13
    • 27744567137 scopus 로고    scopus 로고
    • The computation of bounds for linear-functional outputs of weak solutions to the two-dimensional elasticity equations
    • 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. Computer Methods in Applied Mechanics and Engineering 2006; 195(4-6):406-429.
    • (2006) Computer Methods in Applied Mechanics and Engineering , vol.195 , Issue.4-6 , pp. 406-429
    • Parés, N.1    Bonet, J.2    Huerta, A.3    Peraire, J.4
  • 14
    • 27744563713 scopus 로고    scopus 로고
    • Computing upper and lower bounds for the J-integral in two-dimensional linear elasticity
    • Xuan ZC, Parés N, Peraire J. Computing upper and lower bounds for the J-integral in two-dimensional linear elasticity. Computer Methods in Applied Mechanics and Engineering 2006; 195(46):430-443.
    • (2006) Computer Methods in Applied Mechanics and Engineering , vol.195 , Issue.46 , pp. 430-443
    • Xuan, Z.C.1    Parés, N.2    Peraire, J.3
  • 15
    • 40049096843 scopus 로고    scopus 로고
    • Bounds of functional outputs for parabolic problems. Part I: Exact bounds of the discontinuous Galerkin time discretization
    • Parés N, Díez P, Huerta A. Bounds of functional outputs for parabolic problems. Part I: exact bounds of the discontinuous Galerkin time discretization. Computer Methods in Applied Mechanics and Engineering 2008; 197(19-20):1641-1660.
    • (2008) Computer Methods in Applied Mechanics and Engineering , vol.197 , Issue.19-20 , pp. 1641-1660
    • Parés, N.1    Díez, P.2    Huerta, A.3
  • 16
    • 40049104804 scopus 로고    scopus 로고
    • Bounds of functional outputs for parabolic problems. Part II: Bounds of the exact solution
    • Parés N, Díez P, Huerta A. Bounds of functional outputs for parabolic problems. Part II: bounds of the exact solution. Computer Methods in Applied Mechanics and Engineering 2008; 197(19-20):1661-1679.
    • (2008) Computer Methods in Applied Mechanics and Engineering , vol.197 , Issue.19-20 , pp. 1661-1679
    • Parés, N.1    Díez, P.2    Huerta, A.3
  • 17
    • 33745887468 scopus 로고    scopus 로고
    • Guaranteed and locally computable a posteriori error estimate
    • Vejchodský T. Guaranteed and locally computable a posteriori error estimate. IMA Journal of Numerical Analysis 2006; 26(3):525-540.
    • (2006) IMA Journal of Numerical Analysis , vol.26 , Issue.3 , pp. 525-540
    • Vejchodský, T.1
  • 19
    • 0037436460 scopus 로고    scopus 로고
    • Recovering lower bounds of the error by postprocessing implicit residual a posteriori error estimates
    • Díez P, Parés N, Huerta A. Recovering lower bounds of the error by postprocessing implicit residual a posteriori error estimates. International Journal for Numerical Methods in Engineering 2003; 56(10):1465-1488.
    • (2003) International Journal for Numerical Methods in Engineering , vol.56 , Issue.10 , pp. 1465-1488
    • Díez, P.1    Parés, N.2    Huerta, A.3
  • 20
    • 85044554734 scopus 로고    scopus 로고
    • Strict error bounds for linear solid mechanics problems using a subdomain-based flux-free method
    • accepted for publication
    • Cottereau R, Díez P, Huerta A. Strict error bounds for linear solid mechanics problems using a subdomain-based flux-free method. Computational Mechanics, accepted for publication.
    • Computational Mechanics
    • Cottereau, R.1    Díez, P.2    Huerta, A.3
  • 24
    • 0038129722 scopus 로고    scopus 로고
    • Local problems on stars: A posteriori error estimators, convergence, and performance
    • Morin P, Nochetto R, Siebert K. Local problems on stars: a posteriori error estimators, convergence, and performance. Mathematics of Computation 2003; 72(243):1067-1097.
    • (2003) Mathematics of Computation , vol.72 , Issue.243 , pp. 1067-1097
    • Morin, P.1    Nochetto, R.2    Siebert, K.3
  • 25
    • 33745888462 scopus 로고
    • Conforming equilibrium finite element methods for some elliptic plane problems
    • Křížek M. Conforming equilibrium finite element methods for some elliptic plane problems. RAIRO Analyse Numérique 1983; 17(1):35-65.
    • (1983) RAIRO Analyse Numérique , vol.17 , Issue.1 , pp. 35-65
    • Křížek, M.1
  • 26
    • 0030571233 scopus 로고    scopus 로고
    • Local and pollution error estimation for finite element approximations of elliptic boundary value problems
    • TICAM Symposium (Austin, TX, 1995)
    • Oden JT, Feng Y. Local and pollution error estimation for finite element approximations of elliptic boundary value problems. Journal of Computational and Applied Mathematics 1996; 74(1-2):245-293. TICAM Symposium (Austin, TX, 1995).
    • (1996) Journal of Computational and Applied Mathematics , vol.74 , Issue.1-2 , pp. 245-293
    • Oden, J.T.1    Feng, Y.2
  • 27
    • 1442264993 scopus 로고    scopus 로고
    • A posteriori error estimation for the Poisson equation with mixed Dirichlet/Neumann boundary conditions
    • Proceedings of the 10th International Congress on Computational and Applied Mathematics, (ICCAM- 2002), Belgium
    • Repin S, Sauter S, Smolianski A. A posteriori error estimation for the Poisson equation with mixed Dirichlet/Neumann boundary conditions. Journal of Computational and Applied Mathematics 2004; 164/165: 601-612; Proceedings of the 10th International Congress on Computational and Applied Mathematics (ICCAM- 2002), Belgium, 2002.
    • (2004) Journal of Computational and Applied Mathematics , vol.164-165 , pp. 601-612
    • Repin, S.1    Sauter, S.2    Smolianski, A.3
  • 28
    • 33645521405 scopus 로고    scopus 로고
    • Convergence analysis of an adaptive nonconforming finite element method
    • Carstensen C, Hoppe RHW. Convergence analysis of an adaptive nonconforming finite element method. Numerische Mathematik 2006; 103(2):251-266.
    • (2006) Numerische Mathematik , vol.103 , Issue.2 , pp. 251-266
    • Carstensen, C.1    Hoppe, R.H.W.2
  • 29
    • 0031443748 scopus 로고    scopus 로고
    • A posteriori finite element bounds for linear-functional outputs of elliptic partial differential equations
    • Symposium on Advances in Computational Mechanics, vol. 2 (Austin, TX, 1997)
    • Paraschivoiu M, Peraire J, Patera AT. A posteriori finite element bounds for linear-functional outputs of elliptic partial differential equations. Computer Methods in Applied Mechanics and Engineering 1997; 150(1-4):289-312. Symposium on Advances in Computational Mechanics, vol. 2 (Austin, TX, 1997).
    • (1997) Computer Methods in Applied Mechanics and Engineering , vol.150 , Issue.1-4 , pp. 289-312
    • Paraschivoiu, M.1    Peraire, J.2    Patera, A.T.3


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.