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Volumn 196, Issue 1-3, 2006, Pages 14-23

Adaptive finite elements with large aspect ratio based on an anisotropic error estimator involving first order derivatives

Author keywords

A posteriori error estimates; Adaptive finite elements; Meshes with large aspect ratio

Indexed keywords

ADAPTIVE ALGORITHMS; ASPECT RATIO; COMPUTER SIMULATION; ERROR ANALYSIS; ESTIMATION; FINITE ELEMENT METHOD;

EID: 33846635611     PISSN: 00457825     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.cma.2005.11.018     Document Type: Article
Times cited : (32)

References (39)
  • 1
    • 0031102111 scopus 로고    scopus 로고
    • A posteriori error estimation in finite element analysis
    • Ainsworth M., and Oden J.T. A posteriori error estimation in finite element analysis. Comput. Methods Appl. Mech. Engrg. 142 1-2 (1997) 1-88
    • (1997) Comput. Methods Appl. Mech. Engrg. , vol.142 , Issue.1-2 , pp. 1-88
    • Ainsworth, M.1    Oden, J.T.2
  • 2
    • 0042255750 scopus 로고
    • A unified approach to a posteriori error estimation using finite element residual methods
    • Ainsworth M., and Oden J.T. A unified approach to a posteriori error estimation using finite element residual methods. Numer. Math. 65 (1993) 23-50
    • (1993) Numer. Math. , vol.65 , pp. 23-50
    • Ainsworth, M.1    Oden, J.T.2
  • 3
    • 0024734345 scopus 로고
    • Analysis of the Zienkiewicz-Zhu a posteriori error estimator in the finite element method
    • Ainsworth M., Zhu J.Z., Craig A.W., and Zienkiewicz O.C. Analysis of the Zienkiewicz-Zhu a posteriori error estimator in the finite element method. Internat. J. Numer. Methods Engrg. 28 9 (1989) 2161-2174
    • (1989) Internat. J. Numer. Methods Engrg. , vol.28 , Issue.9 , pp. 2161-2174
    • Ainsworth, M.1    Zhu, J.Z.2    Craig, A.W.3    Zienkiewicz, O.C.4
  • 5
    • 0242666435 scopus 로고    scopus 로고
    • Transient fixed point-based unstructured mesh adaptation
    • ECCOMAS Computational Fluid Dynamics Conference, Part II (Swansea, 2001)
    • Alauzet F., George P.L., Mohammadi B., Frey P., and Borouchaki H. Transient fixed point-based unstructured mesh adaptation. Internat. J. Numer. Methods Fluids 43 6-7 (2003) 729-745 ECCOMAS Computational Fluid Dynamics Conference, Part II (Swansea, 2001)
    • (2003) Internat. J. Numer. Methods Fluids , vol.43 , Issue.6-7 , pp. 729-745
    • Alauzet, F.1    George, P.L.2    Mohammadi, B.3    Frey, P.4    Borouchaki, H.5
  • 6
    • 0034681627 scopus 로고    scopus 로고
    • Adaptive finite element computational fluid dynamics using an anisotropic error estimator
    • IV WCCM (Buenos Aires, 1998)
    • Almeida R.C., Feijóo R.A., Galeão A.C., Padra C., and Silva R.S. Adaptive finite element computational fluid dynamics using an anisotropic error estimator. Comput. Methods Appl. Mech. Engrg. 182 3-4 (2000) 379-400 IV WCCM (Buenos Aires, 1998)
    • (2000) Comput. Methods Appl. Mech. Engrg. , vol.182 , Issue.3-4 , pp. 379-400
    • Almeida, R.C.1    Feijóo, R.A.2    Galeão, A.C.3    Padra, C.4    Silva, R.S.5
  • 7
    • 0026909316 scopus 로고
    • Analysis of the efficiency of an a posteriori error estimator for linear triangular finite elements
    • Babuška I., Duran R., and Rodriguez R. Analysis of the efficiency of an a posteriori error estimator for linear triangular finite elements. SIAM J. Numer. Anal. 29 4 (1992) 947-964
    • (1992) SIAM J. Numer. Anal. , vol.29 , Issue.4 , pp. 947-964
    • Babuška, I.1    Duran, R.2    Rodriguez, R.3
  • 8
    • 0000613724 scopus 로고
    • Error estimates for adaptive finite element computations
    • Babuška I., and Rheinboldt W.C. Error estimates for adaptive finite element computations. SIAM J. Numer. Anal. 15 (1978) 736-754
    • (1978) SIAM J. Numer. Anal. , vol.15 , pp. 736-754
    • Babuška, I.1    Rheinboldt, W.C.2
  • 9
    • 84985315731 scopus 로고
    • A posteriori error estimators in the finite element method
    • Babuška I., and Rheinboldt W.C. A posteriori error estimators in the finite element method. Internat. J. Numer. Meth. Engrg. 12 (1978) 1597-1615
    • (1978) Internat. J. Numer. Meth. Engrg. , vol.12 , pp. 1597-1615
    • Babuška, I.1    Rheinboldt, W.C.2
  • 10
    • 33846630943 scopus 로고    scopus 로고
    • Can we trust the computational analysis of engineering problems?
    • Mathematical Modeling and Numerical Simulation in Continuum Mechanics (Yamaguchi, 2000), Springer, Berlin
    • Babuška I., and Strouboulis T. Can we trust the computational analysis of engineering problems?. Mathematical Modeling and Numerical Simulation in Continuum Mechanics (Yamaguchi, 2000). Lecture Notes in Computer Science Engineering vol. 19 (2002), Springer, Berlin 169-183
    • (2002) Lecture Notes in Computer Science Engineering , vol.19 , pp. 169-183
    • Babuška, I.1    Strouboulis, T.2
  • 12
    • 0030383153 scopus 로고    scopus 로고
    • A feed-back approach to error control in finite element methods: basic analysis and examples
    • Becker R., and Rannacher R. A feed-back approach to error control in finite element methods: basic analysis and examples. East-West J. Numer. Math. 4 4 (1996) 237-264
    • (1996) East-West J. Numer. Math. , vol.4 , Issue.4 , pp. 237-264
    • Becker, R.1    Rannacher, R.2
  • 13
    • 33846566381 scopus 로고    scopus 로고
    • H. Borouchaki, P. Laug. The BL2D mesh generator: Beginner's guide, user's and programmer's manual, Technical Report RT-0194, Institut National de Recherche en Informatique et Automatique (INRIA), Rocquencourt, 78153 Le Chesnay, France, 1996.
  • 14
    • 0345447627 scopus 로고    scopus 로고
    • Gradient superconvergence on uniform simplicial partitions of polytopes
    • Brandts J., and Křížek M. Gradient superconvergence on uniform simplicial partitions of polytopes. IMA J. Numer. Anal. 23 3 (2003) 489-505
    • (2003) IMA J. Numer. Anal. , vol.23 , Issue.3 , pp. 489-505
    • Brandts, J.1    Křížek, M.2
  • 15
    • 1542531175 scopus 로고    scopus 로고
    • Adaptive finite elements with high aspect ratio for the computation of coalescence using a phase-field model
    • Burman E., Jacot A., and Picasso M. Adaptive finite elements with high aspect ratio for the computation of coalescence using a phase-field model. J. Comput. Phys. 195 1 (2004) 153-174
    • (2004) J. Comput. Phys. , vol.195 , Issue.1 , pp. 153-174
    • Burman, E.1    Jacot, A.2    Picasso, M.3
  • 16
    • 85006910088 scopus 로고    scopus 로고
    • Anisotropic, adaptive finite elements for the computation of a solutal dendrite
    • Burman E., and Picasso M. Anisotropic, adaptive finite elements for the computation of a solutal dendrite. J. Interfaces Free Bound. 5 (2003) 103-127
    • (2003) J. Interfaces Free Bound. , vol.5 , pp. 103-127
    • Burman, E.1    Picasso, M.2
  • 17
    • 2942651067 scopus 로고    scopus 로고
    • All first-order averaging techniques for a posteriori finite element error control on unstructured grids are efficient and reliable
    • Carstensen C. All first-order averaging techniques for a posteriori finite element error control on unstructured grids are efficient and reliable. Math. Comp. 73 247 (2004) 1153-1165
    • (2004) Math. Comp. , vol.73 , Issue.247 , pp. 1153-1165
    • Carstensen, C.1
  • 18
    • 0016541865 scopus 로고
    • Approximation by finite element functions using local regularization
    • Clément P. Approximation by finite element functions using local regularization. RAIRO Anal. Numér. 9 (1975) 77-84
    • (1975) RAIRO Anal. Numér. , vol.9 , pp. 77-84
    • Clément, P.1
  • 19
    • 33846641305 scopus 로고    scopus 로고
    • Distene S.A.S., Pôle Teratec - BARD-1, Domaine du Grand Rué, 91680 Bruyères-le-Chatel, France. MeshAdapt: A mesh adaptation tool, User's manual Version 3.0, 2003.
  • 20
    • 0035602908 scopus 로고    scopus 로고
    • New anisotropic a priori error estimates
    • Formaggia L., and Perotto S. New anisotropic a priori error estimates. Numer. Math. 89 4 (2001) 641-667
    • (2001) Numer. Math. , vol.89 , Issue.4 , pp. 641-667
    • Formaggia, L.1    Perotto, S.2
  • 21
    • 0142118651 scopus 로고    scopus 로고
    • Anisotropic error estimates for elliptic problems
    • Formaggia L., and Perotto S. Anisotropic error estimates for elliptic problems. Numer. Math. 94 (2003) 67-92
    • (2003) Numer. Math. , vol.94 , pp. 67-92
    • Formaggia, L.1    Perotto, S.2
  • 23
    • 14544277377 scopus 로고    scopus 로고
    • Adaptive finite element methods for incompressible fluid flow
    • Error Estimation and Adaptive Discretization Methods in Computational Fluid Dynamics, Springer, Berlin
    • Hoffman J., and Johnson C. Adaptive finite element methods for incompressible fluid flow. Error Estimation and Adaptive Discretization Methods in Computational Fluid Dynamics. Lecture Notes Computer Science Engrg vol. 25 (2003), Springer, Berlin 97-157
    • (2003) Lecture Notes Computer Science Engrg , vol.25 , pp. 97-157
    • Hoffman, J.1    Johnson, C.2
  • 24
    • 0034394001 scopus 로고    scopus 로고
    • An a posteriori residual error estimator for the finite element method on anisotropic tetrahedral meshes
    • Kunert G. An a posteriori residual error estimator for the finite element method on anisotropic tetrahedral meshes. Numer. Math. 86 3 (2000) 471-490
    • (2000) Numer. Math. , vol.86 , Issue.3 , pp. 471-490
    • Kunert, G.1
  • 25
    • 0346946991 scopus 로고    scopus 로고
    • Zienkiewicz-Zhu error estimators on anisotropic tetrahedral and triangular finite element meshes
    • Kunert G., and Nicaise S. Zienkiewicz-Zhu error estimators on anisotropic tetrahedral and triangular finite element meshes. M2AN Math. Model. Numer. Anal. 37 6 (2003) 1013-1043
    • (2003) M2AN Math. Model. Numer. Anal. , vol.37 , Issue.6 , pp. 1013-1043
    • Kunert, G.1    Nicaise, S.2
  • 26
    • 0039372640 scopus 로고    scopus 로고
    • Edge residuals dominate a posteriori error estimates for linear finite element methods on anisotropic triangular and tetrahedral meshes
    • Kunert G., and Verfürth R. Edge residuals dominate a posteriori error estimates for linear finite element methods on anisotropic triangular and tetrahedral meshes. Numer. Math. 86 2 (2000) 283-303
    • (2000) Numer. Math. , vol.86 , Issue.2 , pp. 283-303
    • Kunert, G.1    Verfürth, R.2
  • 27
    • 3142737182 scopus 로고    scopus 로고
    • Stabilized finite elements on anisotropic meshes: a priori error estimates for the advection-diffusion and the Stokes problems
    • Micheletti S., Perotto S., and Picasso M. Stabilized finite elements on anisotropic meshes: a priori error estimates for the advection-diffusion and the Stokes problems. SIAM J. Numer. Anal. 41 3 (2003) 1131-1162
    • (2003) SIAM J. Numer. Anal. , vol.41 , Issue.3 , pp. 1131-1162
    • Micheletti, S.1    Perotto, S.2    Picasso, M.3
  • 28
    • 23844507571 scopus 로고    scopus 로고
    • A posteriori error estimates based on the polynomial preserving recovery
    • (electronic)
    • Naga A., and Zhang Z. A posteriori error estimates based on the polynomial preserving recovery. SIAM J. Numer. Anal. 42 4 (2004) 1780-1800 (electronic)
    • (2004) SIAM J. Numer. Anal. , vol.42 , Issue.4 , pp. 1780-1800
    • Naga, A.1    Zhang, Z.2
  • 29
    • 0037280081 scopus 로고    scopus 로고
    • Numerical study of the effectivity index for an anisotropic error indicator based on Zienkiewicz-Zhu error estimator
    • Picasso M. Numerical study of the effectivity index for an anisotropic error indicator based on Zienkiewicz-Zhu error estimator. Comm. Numer. Methods Engrg. 19 (2002) 13-23
    • (2002) Comm. Numer. Methods Engrg. , vol.19 , pp. 13-23
    • Picasso, M.1
  • 30
    • 0042931313 scopus 로고    scopus 로고
    • An anisotropic error indicator based on Zienkiewicz-Zhu error estimator: application to elliptic and parabolic problems
    • Picasso M. An anisotropic error indicator based on Zienkiewicz-Zhu error estimator: application to elliptic and parabolic problems. SIAM J. Sci. Comp. 24 (2003) 1328-1355
    • (2003) SIAM J. Sci. Comp. , vol.24 , pp. 1328-1355
    • Picasso, M.1
  • 31
    • 14344265344 scopus 로고    scopus 로고
    • Anisotropic adaptive simulation of transient flows using discontinuous Galerkin methods
    • Remacle J.-F., Li X., Shephard M.S., and Flaherty J.E. Anisotropic adaptive simulation of transient flows using discontinuous Galerkin methods. Int. J. Numer. Methods Engrg. 62 7 (2005) 899-923
    • (2005) Int. J. Numer. Methods Engrg. , vol.62 , Issue.7 , pp. 899-923
    • Remacle, J.-F.1    Li, X.2    Shephard, M.S.3    Flaherty, J.E.4
  • 33
    • 0035282142 scopus 로고    scopus 로고
    • A review of algebraic multigrid
    • Numerical analysis 2000, Vol. VII, Partial differential equations
    • Stüben K. A review of algebraic multigrid. J. Comput. Appl. Math. 128 1 (2001) 281-309 Numerical analysis 2000, Vol. VII, Partial differential equations
    • (2001) J. Comput. Appl. Math. , vol.128 , Issue.1 , pp. 281-309
    • Stüben, K.1
  • 34
    • 0041034172 scopus 로고    scopus 로고
    • Convergence of algebraic multigrid based on smoothed aggregation
    • Vaněk P., Brezina M., and Mandel J. Convergence of algebraic multigrid based on smoothed aggregation. Numer. Math. 88 3 (2001) 559-579
    • (2001) Numer. Math. , vol.88 , Issue.3 , pp. 559-579
    • Vaněk, P.1    Brezina, M.2    Mandel, J.3
  • 36
    • 33846641764 scopus 로고    scopus 로고
    • J. Xu, Z. Zhang, Analysis of recovery type a posteriori error estimators for midly structured grids, Math. Comp. Electronically published, 2003.
  • 37
    • 23844471344 scopus 로고    scopus 로고
    • A new finite element gradient recovery method: superconvergence property
    • (electronic)
    • Zhang Z., and Naga A. A new finite element gradient recovery method: superconvergence property. SIAM J. Sci. Comput. 26 4 (2005) 1192-1213 (electronic)
    • (2005) SIAM J. Sci. Comput. , vol.26 , Issue.4 , pp. 1192-1213
    • Zhang, Z.1    Naga, A.2
  • 38
    • 0023288565 scopus 로고
    • A simple error estimator and adaptive procedure for practical engineering analysis
    • Zienkiewicz O.C., and Zhu J.Z. A simple error estimator and adaptive procedure for practical engineering analysis. Int. J. Numer. Methods Engrg. 24 2 (1987) 337-357
    • (1987) Int. J. Numer. Methods Engrg. , vol.24 , Issue.2 , pp. 337-357
    • Zienkiewicz, O.C.1    Zhu, J.Z.2
  • 39
    • 0026866050 scopus 로고
    • The superconvergent patch recovery and a posteriori error estimates. I. The recovery technique
    • Zienkiewicz O.C., and Zhu J.Z. The superconvergent patch recovery and a posteriori error estimates. I. The recovery technique. Int. J. Numer. Methods Engrg. 33 7 (1992) 1331-1364
    • (1992) Int. J. Numer. Methods Engrg. , vol.33 , Issue.7 , pp. 1331-1364
    • Zienkiewicz, O.C.1    Zhu, J.Z.2


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