메뉴 건너뛰기




Volumn 21, Issue 2, 2001, Pages 503-523

A posteriori L2 error estimation on anisotropic tetrahedral finite element meshes

Author keywords

Anisotropic mesh; Anisotropic solution; L2error estimation; Tetrahedral element

Indexed keywords

BOUNDARY CONDITIONS; ERROR ANALYSIS; FINITE ELEMENT METHOD; INVERSE PROBLEMS; MESH GENERATION; NUMERICAL METHODS; POISSON EQUATION;

EID: 0035531730     PISSN: 02724979     EISSN: None     Source Type: Journal    
DOI: 10.1093/imanum/21.2.503     Document Type: Article
Times cited : (14)

References (23)
  • 1
    • 0031102111 scopus 로고    scopus 로고
    • A posteriori error estimation in finite element analysis
    • AINSWORTH, M. & ODEN, J. T. 1997 A posteriori error estimation in finite element analysis. Comput. Methods Appl. Mech. Eng., 142, 1-88.
    • (1997) Comput. Methods Appl. Mech. Eng. , vol.142 , pp. 1-88
    • Ainsworth, M.1    Oden, J.T.2
  • 2
    • 0033270542 scopus 로고    scopus 로고
    • Interpolation of non-smooth functions on anisotropic finite element meshes
    • APEL, TH. 1999 Interpolation of non-smooth functions on anisotropic finite element meshes. Math. Modeling Numer. Anal., 33, 1149-1185.
    • (1999) Math. Modeling Numer. Anal. , vol.33 , pp. 1149-1185
    • Apel, T.H.1
  • 3
    • 0026626564 scopus 로고
    • Anisotropic interpolation with applications to the finite element method
    • APEL, TH. & DOBROWOLSKI, M. 1992 Anisotropic interpolation with applications to the finite element method. Computing, 47, 277-293.
    • (1992) Computing , vol.47 , pp. 277-293
    • Apel, T.H.1    Dobrowolski, M.2
  • 4
    • 0000620759 scopus 로고
    • Behaviour of the error of the approximate solution of boundary value problems for linear elliptic operators by Galerkin's and finite difference methods
    • AUBIN, J. P. 1967 Behaviour of the error of the approximate solution of boundary value problems for linear elliptic operators by Galerkin's and finite difference methods. Ann. Scuola Norm. Sup. Pisa, 21, 599-637.
    • (1967) Ann. Scuola Norm. Sup. Pisa , vol.21 , pp. 599-637
    • Aubin, J.P.1
  • 5
    • 84985315731 scopus 로고
    • A posteriori error estimates for the finite element method
    • BABUŠKA, I. & RHEINBOLDT, W. C. 1978 A posteriori error estimates for the finite element method. Int. J. Numer. Methods Eng., 12, 1597-1615.
    • (1978) Int. J. Numer. Methods Eng. , vol.12 , pp. 1597-1615
    • Babuška, I.1    Rheinboldt, W.C.2
  • 6
    • 0027642848 scopus 로고
    • A posteriori estimates based on hierarchical basis
    • BANK, R. E. & SMITH, R. K. 1993 A posteriori estimates based on hierarchical basis. SIAM J. Numer. Anal., 30, 921-935.
    • (1993) SIAM J. Numer. Anal. , vol.30 , pp. 921-935
    • Bank, R.E.1    Smith, R.K.2
  • 7
    • 84966215690 scopus 로고
    • Some a posteriori error estimators for elliptic partial differential equations
    • BANK, R. E. & WEISER, A. 1985 Some a posteriori error estimators for elliptic partial differential equations. Math. Comput., 44, 283-301.
    • (1985) Math. Comput. , vol.44 , pp. 283-301
    • Bank, R.E.1    Weiser, A.2
  • 8
    • 0030383153 scopus 로고    scopus 로고
    • A feed-back approach to error control in finite element methods: Basic analysis and examples
    • BECKER, R. & RANNACHER, R. 1996 A feed-back approach to error control in finite element methods: Basic analysis and examples. East-West J. Numer. Math., 4, 237-264.
    • (1996) East-West J. Numer. Math. , vol.4 , pp. 237-264
    • Becker, R.1    Rannacher, R.2
  • 9
    • 0001701058 scopus 로고    scopus 로고
    • A posteriori error estimates for elliptic problems in two and three space dimensions
    • BORNEMANN, F., ERDMANN, B., & KORNHUBER, R. 1996 A posteriori error estimates for elliptic problems in two and three space dimensions. SIAM J. Num. Anal., 33, 1188-1204.
    • (1996) SIAM J. Num. Anal. , vol.33 , pp. 1188-1204
    • Bornemann, F.1    Erdmann, B.2    Kornhuber, R.3
  • 11
    • 0003140025 scopus 로고    scopus 로고
    • On a posteriori error estimators in the finite element method on anisotropic meshes
    • DOBROWOLSKI, M., GRÄF, S., & PFLAUM, C. 1999 On a posteriori error estimators in the finite element method on anisotropic meshes. Electronic Transactions Numer. Anal., 8, 36-45.
    • (1999) Electronic Transactions Numer. Anal. , vol.8 , pp. 36-45
    • Dobrowolski, M.1    Gräf, S.2    Pflaum, C.3
  • 12
    • 0026106415 scopus 로고
    • Adaptive finite element methods for parabolic problems I: A linear model problem
    • ERIKSSON, K., & JOHNSON, C. 1991 Adaptive finite element methods for parabolic problems I: A linear model problem. SIAM J. Numer. Anal., 28, 43-77.
    • (1991) SIAM J. Numer. Anal. , vol.28 , pp. 43-77
    • Eriksson, K.1    Johnson, C.2
  • 13
    • 0001829437 scopus 로고
    • On adaptive grid refinement in the presence of internal and boundary layers
    • KORNHUBER, R. & ROITZSCH, R. 1990 On adaptive grid refinement in the presence of internal and boundary layers. IMPACT of Comput. Sci. Eng., 2, 40-72.
    • (1990) IMPACT of Comput. Sci. Eng. , vol.2 , pp. 40-72
    • Kornhuber, R.1    Roitzsch, R.2
  • 15
    • 0034394001 scopus 로고    scopus 로고
    • An a posteriori residual error estimator for the finite element method on anisotropic tetrahedral meshes
    • KUNERT, G. 2000a An a posteriori residual error estimator for the finite element method on anisotropic tetrahedral meshes. Numer. Math., 86, 471-490.
    • (2000) Numer. Math. , vol.86 , pp. 471-490
    • Kunert, G.1
  • 17
    • 0039372640 scopus 로고    scopus 로고
    • Edge residuals dominate a posteriori error estimates for linear finite element methods on anisotropic triangular and tetrahedral meshes
    • DOI 10.1007/s002110000152
    • KUNERT, G. & VERFÜRTH, R. 2000 Edge residuals dominate a posteriori error estimates for linear finite element methods on anisotropic triangular and tetrahedral meshes. Numer. Math., 86, 283-303 DOI 10.1007/s002110000152.
    • (2000) Numer. Math. , vol.86 , pp. 283-303
    • Kunert, G.1    Verfürth, R.2
  • 18
    • 0007226236 scopus 로고
    • Ein kriterium für die Quasi-Optimalität des ritzschen verfahrens
    • NITSCHE, J. A. 1968 Ein Kriterium für die Quasi-Optimalität des Ritzschen Verfahrens. Numer. Mart., 21, 138-160.
    • (1968) Numer. Mart. , vol.21 , pp. 138-160
    • Nitsche, J.A.1
  • 20
    • 0030530686 scopus 로고    scopus 로고
    • An a posteriori error estimator for anisotropic refinement
    • SIEBERT, K. G. 1996 An a posteriori error estimator for anisotropic refinement. Numer. Math., 73, 373-398.
    • (1996) Numer. Math. , vol.73 , pp. 373-398
    • Siebert, K.G.1
  • 22
    • 0023288565 scopus 로고
    • A simple error estimator and adaptive procedure for practical engineering analysis
    • ZIENKIEWICZ, O. C. & ZHU, J. Z. 1987 A simple error estimator and adaptive procedure for practical engineering analysis. Int. J. Numer. Methods Eng., 24, 337-357.
    • (1987) Int. J. Numer. Methods Eng. , vol.24 , pp. 337-357
    • Zienkiewicz, O.C.1    Zhu, J.Z.2
  • 23
    • 0026981573 scopus 로고
    • The superconvergent patch recovery (SPR) and adaptive finite element refinement
    • ZIENKIEWICZ, O. C. & ZHU, J. Z. 1992 The superconvergent patch recovery (SPR) and adaptive finite element refinement. Comput. Methods Appl. Mech. Eng., 101, 207-224.
    • (1992) Comput. Methods Appl. Mech. Eng. , vol.101 , pp. 207-224
    • Zienkiewicz, O.C.1    Zhu, J.Z.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.