메뉴 건너뛰기




Volumn 24, Issue 4, 2003, Pages 1328-1355

An anisotropic error indicator based on Zienkiewicz-Zhu error estimator: Application to elliptic and parabolic problems

Author keywords

Adaptive finite elements; Anisotropic a posteriori error estimates

Indexed keywords

ADAPTIVE ALGORITHMS; FINITE ELEMENT METHOD; INTERPOLATION; LAPLACE TRANSFORMS; MATRIX ALGEBRA; PROBLEM SOLVING;

EID: 0042931313     PISSN: 10648275     EISSN: None     Source Type: Journal    
DOI: 10.1137/S1064827501398578     Document Type: Article
Times cited : (99)

References (34)
  • 1
    • 0031102111 scopus 로고    scopus 로고
    • A posteriori error estimation in finite element analysis
    • M. AINSWORTH AND J. T. ODEN, A posteriori error estimation in finite element analysis, Comput. Methods Appl. Mech. Engrg., 142 (1997), pp. 1-88.
    • (1997) Comput. Methods Appl. Mech. Engrg. , vol.142 , pp. 1-88
    • 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
    • M. AINSWORTH, J. Z. ZHU, A. W. CRAIG, AND O. C. ZIENKIEWICZ, Analysis of the Zienkiewicz-Zhu a posteriori error estimator in the finite element method, Internat. J. Numer. Methods Engrg., 28 (1989), pp. 2161-2174.
    • (1989) Internat. J. Numer. Methods Engrg. , vol.28 , pp. 2161-2174
    • Ainsworth, M.1    Zhu, J.Z.2    Craig, A.W.3    Zienkiewicz, O.C.4
  • 5
    • 0026909316 scopus 로고
    • Analysis of the efficiency of an a posteriori error estimator for linear triangular finite elements
    • I. BABUŠKA, R. DURÁN, AND R. RODRÍGUEZ, Analysis of the efficiency of an a posteriori error estimator for linear triangular finite elements, SIAM J. Numer. Anal., 29 (1992), pp. 947-964.
    • (1992) SIAM J. Numer. Anal. , vol.29 , pp. 947-964
    • Babuška, I.1    Durán, R.2    Rodríguez, R.3
  • 6
    • 0028407162 scopus 로고
    • A model study of the quality of a posteriori estimators for linear elliptic problems. Error estimation in the interior of patchwise uniform grids of triangles
    • I. BABUŠKA, T. STROUBOULIS, AND C. S. UPADHYAY, A model study of the quality of a posteriori estimators for linear elliptic problems. Error estimation in the interior of patchwise uniform grids of triangles, Comput. Methods Appl. Mech. Engrg., 114 (1994), pp. 307-378.
    • (1994) Comput. Methods Appl. Mech. Engrg. , vol.114 , pp. 307-378
    • Babuška, I.1    Strouboulis, T.2    Upadhyay, C.S.3
  • 7
    • 0001883660 scopus 로고
    • Estimateurs a posteriori d'erreur pour le calcul adaptatif d'écoulements quasi-newtoniens
    • J. BARANGER AND H. EL-AMRI, Estimateurs a posteriori d'erreur pour le calcul adaptatif d'écoulements quasi-newtoniens, RAIRO Modél Math. Anal. Numér., 25 (1991), pp. 31-48.
    • (1991) RAIRO Modél Math. Anal. Numér. , vol.25 , pp. 31-48
    • Baranger, J.1    El-Amri, H.2
  • 8
    • 0003491412 scopus 로고    scopus 로고
    • The BL2D mesh generator: Beginner's guide, user's and programmer's manual
    • Institut National de Recherche en Informatique et Automatique (INRIA), Rocquencourt, 78153 Le Chesnay, France
    • H. BOROUCHAKI AND 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.
    • (1996) Technical Report , vol.RT-0194
    • Borouchaki, H.1    Laug, P.2
  • 9
    • 85160587852 scopus 로고    scopus 로고
    • Anisotropic, adaptive finite elements for the computation of a solutal dendrite
    • Département de Mathématiques, Ecole Polytechnique Fédérale de Lausanne, 1015 Lausanne, Switzerland
    • E. BURMAN AND M. PICASSO, Anisotropic, Adaptive Finite Elements for the Computation of a Solutal Dendrite; Technical report, Département de Mathématiques, Ecole Polytechnique Fédérale de Lausanne, 1015 Lausanne, Switzerland, 2002
    • (2002) Technical Report
    • Burman, E.1    Picasso, M.2
  • 11
    • 0004143319 scopus 로고
    • Analyse mathématique et calcul numérique pour les sciences et les techniques
    • Masson, Paris
    • R. DAUTRAY AND J.-L. LIONS, Analyse mathématique et calcul numérique pour les sciences et les techniques, INSTN. Collection Enseignement, Masson, Paris, 1988.
    • (1988) INSTN. Collection Enseignement
    • Dautray, R.1    Lions, J.-L.2
  • 12
    • 0042824284 scopus 로고    scopus 로고
    • Anisotropic error estimates for elliptic problems
    • DOI 10.1007/s002110200415
    • L. FORMAGGIA AND S. PEROTTO, Anisotropic error estimates for elliptic problems, Numer. Math., (2002), DOI 10.1007/s002110200415.
    • (2002) Numer. Math.
    • Formaggia, L.1    Perotto, S.2
  • 13
    • 0035602908 scopus 로고    scopus 로고
    • New anisotropic a priori error estimates
    • L. FORMAGGIA AND S. PEROTTO, New anisotropic a priori error estimates, Numer. Math., 89 (2001), pp. 641-667.
    • (2001) Numer. Math. , vol.89 , pp. 641-667
    • Formaggia, L.1    Perotto, S.2
  • 14
    • 0026835579 scopus 로고
    • Stabilized finite element methods. I. Application to the advective-diffusive model
    • L. P. FRANCA, S. L. FREY, AND T. J. R. HUGHES, Stabilized finite element methods. I. Application to the advective-diffusive model, Comput. Methods Appl. Mech. Engrg., 95 (1992), pp. 253-276.
    • (1992) Comput. Methods Appl. Mech. Engrg. , vol.95 , pp. 253-276
    • Franca, L.P.1    Frey, S.L.2    Hughes, T.J.R.3
  • 16
    • 0040366472 scopus 로고    scopus 로고
    • Stabilized Galerkin methods and layer-adapted grids for elliptic problems
    • R. HANGLEITER AND G. LUBE, Stabilized Galerkin methods and layer-adapted grids for elliptic problems, Comput. Methods Appl. Mech. Engrg., 166 (1998), pp. 165-182.
    • (1998) Comput. Methods Appl. Mech. Engrg. , vol.166 , pp. 165-182
    • Hangleiter, R.1    Lube, G.2
  • 17
    • 0035529763 scopus 로고    scopus 로고
    • The reliability of local error estimators for convection-diffusion equations
    • D. KAY AND D. SILVESTER, The reliability of local error estimators for convection-diffusion equations, IMA J. Numer. Anal., 21 (2001), pp. 107-122.
    • (2001) IMA J. Numer. Anal. , vol.21 , pp. 107-122
    • Kay, D.1    Silvester, D.2
  • 18
    • 0040495251 scopus 로고
    • Finite element approximation for a div-rot system with mixed boundary conditions in nonsmooth plane domains
    • M. KŘÍŽEK AND P. NEITTAANMÄKI, Finite element approximation for a div-rot system with mixed boundary conditions in nonsmooth plane domains, Apl. Mat., 29 (1984), pp. 272-285.
    • (1984) Apl. Mat. , vol.29 , pp. 272-285
    • Křížek, M.1    Neittaanmäki, P.2
  • 19
    • 0035531730 scopus 로고    scopus 로고
    • 2 error estimation on anisotropic tetrahedral finite element meshes
    • 2 error estimation on anisotropic tetrahedral finite element meshes, IMA J. Numer. Anal., 21 (2001), pp. 503-523.
    • (2001) IMA J. Numer. Anal. , vol.21 , pp. 503-523
    • Kunert, G.1
  • 20
    • 85160615389 scopus 로고    scopus 로고
    • A posteriori error estimation for convection dominated problems on anisotropic meshes
    • to appear
    • G. KUNERT, A posteriori error estimation for convection dominated problems on anisotropic meshes, Math. Methods Appl. Sci., to appear.
    • Math. Methods Appl. Sci.
    • Kunert, G.1
  • 21
    • 0030511355 scopus 로고    scopus 로고
    • Error estimates and adaptive finite elements for nonlinear diffusion-convection problems
    • J. MEDINA, M. PICASSO, AND J. RAPPAZ, Error estimates and adaptive finite elements for nonlinear diffusion-convection problems, Math. Models Methods Appl. Sci., 6 (1996), pp. 689-712.
    • (1996) Math. Models Methods Appl. Sci. , vol.6 , pp. 689-712
    • Medina, J.1    Picasso, M.2    Rappaz, J.3
  • 22
    • 85160595105 scopus 로고    scopus 로고
    • Some remarks on the stability coefficients and bubble stabilizations of fem on anisotropic meshes
    • Technical Report, MOX, Dipartimento di Matematica, Politecnico di Milano, Italy
    • S. MICHELETTI, S. PEROTTO, AND M. PICASSO, Some Remarks on the Stability Coefficients and Bubble Stabilizations of fem on Anisotropic Meshes, Technical report, MOX, Dipartimento di Matematica, Politecnico di Milano, Italy, 2002, submitted to Comput. Visualization Sci.
    • (2002) Comput. Visualization Sci.
    • Micheletti, S.1    Perotto, S.2    Picasso, M.3
  • 23
    • 85160608455 scopus 로고    scopus 로고
    • Stabilized finite elements on anisotropic meshes: A priori error estimates for the advection-diffusion and Stokes problem
    • MOX, Dipartimento di Matematica, Politecnico di Milano, Italy
    • S. MICHELETTI, S. PEROTTO, AND M. PICASSO, Stabilized finite elements on anisotropic meshes: A priori error estimates for the advection-diffusion and Stokes problem, Technical report, MOX, Dipartimento di Matematica, Politecnico di Milano, Italy, 2002
    • (2002) Technical Report
    • Micheletti, S.1    Perotto, S.2    Picasso, M.3
  • 25
    • 84966202728 scopus 로고
    • An adaptive finite element method for two-phase stefan problems in two space dimensions. Part i
    • R. H. NOCHETTO, M. PAOLINI, AND C. VERDI, An adaptive finite element method for two-phase stefan problems in two space dimensions. Part i, Math. Comp., 57 (1991), pp. 73-108.
    • (1991) Math. Comp. , vol.57 , pp. 73-108
    • Nochetto, R.H.1    Paolini, M.2    Verdi, C.3
  • 26
    • 0032308963 scopus 로고    scopus 로고
    • Adaptive finite elements for a linear parabolic problem
    • M. PICASSO, Adaptive finite elements for a linear parabolic problem, Comput. Methods Appl. Mech. Engrg., 167 (1998), pp. 223-237.
    • (1998) Comput. Methods Appl. Mech. Engrg. , vol.167 , pp. 223-237
    • Picasso, M.1
  • 27
    • 0037280081 scopus 로고    scopus 로고
    • Numerical study of the effectivity index for an anisotropic error indicator based on Zienkiewicz-Zhu error estimator
    • M. PICASSO, Numerical study of the effectivity index for an anisotropic error indicator based on Zienkiewicz-Zhu error estimator, Comm. Numer. Methods Engrg., 19 (2003), pp. 13-23.
    • (2003) Comm. Numer. Methods Engrg. , vol.19 , pp. 13-23
    • Picasso, M.1
  • 29
    • 0030530686 scopus 로고    scopus 로고
    • An a posteriori error estimator for anisotropic refinement
    • K. G. SIEBERT, An a posteriori error estimator for anisotropic refinement, Numer. Math., 73 (1996), pp. 373-398.
    • (1996) Numer. Math. , vol.73 , pp. 373-398
    • Siebert, K.G.1
  • 30
    • 34249971216 scopus 로고
    • A posteriori error estimators for the Stokes equations
    • R. VERFÜRTH, A posteriori error estimators for the Stokes equations, Numer. Math., 55 (1989), pp. 309-325.
    • (1989) Numer. Math. , vol.55 , pp. 309-325
    • Verfürth, R.1
  • 32
    • 0038855305 scopus 로고    scopus 로고
    • A posteriori error estimators for convection-diffusion equations
    • R. VERFÜRTH, A posteriori error estimators for convection-diffusion equations, Numer. Math., 80 (1998), pp. 641-663.
    • (1998) Numer. Math. , vol.80 , pp. 641-663
    • Verfürth, R.1
  • 33
    • 0023288565 scopus 로고
    • A simple error estimator and adaptive procedure for practical engineering analysis
    • O. C. ZIENKIEWICZ AND J. Z. ZHU, A simple error estimator and adaptive procedure for practical engineering analysis, Internat. J. Numer. Methods Engrg., 24 (1987), pp. 337-357.
    • (1987) Internat. J. Numer. Methods Engrg. , vol.24 , pp. 337-357
    • Zienkiewicz, O.C.1    Zhu, J.Z.2
  • 34
    • 0026866050 scopus 로고
    • The superconvergent patch recovery and a posteriori error estimates. I. The recovery technique
    • O. C. ZIENKIEWICZ AND J. Z. ZHU, The superconvergent patch recovery and a posteriori error estimates. I. The recovery technique, Internat. J. Numer. Methods Engrg., 33 (1992), pp. 1331-1364.
    • (1992) Internat. J. Numer. Methods Engrg. , vol.33 , pp. 1331-1364
    • Zienkiewicz, O.C.1    Zhu, J.Z.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.