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Volumn 12, Issue 2, 2004, Pages 143-167

An implicit interpolation error-based error estimation strategy for hp-adaptivity in one space dimension

Author keywords

A posteriori error estimation; Adaptive refinement

Indexed keywords

A POSTERIORI ERROR ESTIMATION; ADAPTIVE REFINEMENT; PARABOLIC EQUATIONS; REACTION-DIFFUSION PROBLEMS;

EID: 2942567900     PISSN: 15702820     EISSN: None     Source Type: Journal    
DOI: 10.1163/156939504323074522     Document Type: Article
Times cited : (4)

References (28)
  • 1
    • 21144473419 scopus 로고
    • A posteriori error estimation with finite element methods of lines for one-dimensional parabolic systems
    • S. Adjerid, J. E. Flaherty, and Y. J. Wang, A posteriori error estimation with finite element methods of lines for one-dimensional parabolic systems. Numer. Math. (1993) 65, 1-21.
    • (1993) Numer. Math. , vol.65 , pp. 1-21
    • Adjerid, S.1    Flaherty, J.E.2    Wang, Y.J.3
  • 2
    • 0033410127 scopus 로고    scopus 로고
    • A posteriori error estimation for the finite element method-of-lines solution of parabolic problems
    • S. Adjerid, I. Babǔska, and J. E. Flaherty, A posteriori error estimation for the finite element method-of-lines solution of parabolic problems. Math. Model. Meth. Appl. Sci. (1999) 9, 261-286.
    • (1999) Math. Model. Meth. Appl. Sci. , vol.9 , pp. 261-286
    • Adjerid, S.1    Babǔska, I.2    Flaherty, J.E.3
  • 3
    • 0033293882 scopus 로고    scopus 로고
    • A posteriori error estimation for diffusion systems
    • S. Adjerid, B. Belguendouz, and J. E. Flaherty, A posteriori error estimation for diffusion systems, SIAM J. Sci. Comp. (1999) 21, 728-746.
    • (1999) SIAM J. Sci. Comp. , vol.21 , pp. 728-746
    • Adjerid, S.1    Belguendouz, B.2    Flaherty, J.E.3
  • 5
    • 0035630248 scopus 로고    scopus 로고
    • On one approach to a posteriori error estimates for evolution problems solved by the methods of lines
    • I. Babǔska, M. Feistauer, and P. Šolín, On one approach to a posteriori error estimates for evolution problems solved by the methods of lines. Numer. Math. (2001) 89, 225-256.
    • (2001) Numer. Math. , vol.89 , pp. 225-256
    • Babǔska, I.1    Feistauer, M.2    Šolín, P.3
  • 8
    • 84904150653 scopus 로고
    • Adaptive finite element methods for parabolic problems, IV. Nonlinear problems
    • K. Eriksson and C. Johnson, Adaptive finite element methods for parabolic problems, IV. Nonlinear problems. SIAM J. Numer. Anal. (1995) 32, 1729-1749.
    • (1995) SIAM J. Numer. Anal. , vol.32 , pp. 1729-1749
    • Eriksson, K.1    Johnson, C.2
  • 10
    • 0000871598 scopus 로고
    • Integrated space-time adaptive hp-refinement methods for parabolic systems
    • J. E. Flaherty and P. K. Moore, Integrated space-time adaptive hp-refinement methods for parabolic systems. Appl. Numer. Math. (1995) 16, 317-341.
    • (1995) Appl. Numer. Math. , vol.16 , pp. 317-341
    • Flaherty, J.E.1    Moore, P.K.2
  • 11
    • 0028374973 scopus 로고
    • A posteriori error estimation with finite element semi- and fully-discrete methods for nonlinear parabolic equations in one space dimension
    • P. K. Moore, A posteriori error estimation with finite element semi- and fully-discrete methods for nonlinear parabolic equations in one space dimension. SIAM J. Numer. Anal. (1994) 31, 149-169.
    • (1994) SIAM J. Numer. Anal. , vol.31 , pp. 149-169
    • Moore, P.K.1
  • 12
    • 0000646363 scopus 로고
    • Comparison of adaptive methods for one-dimensional parabolic systems
    • P. K. Moore, Comparison of adaptive methods for one-dimensional parabolic systems. Appl. Numer. Math. (1995) 16, 471-488.
    • (1995) Appl. Numer. Math. , vol.16 , pp. 471-488
    • Moore, P.K.1
  • 13
    • 0035540060 scopus 로고    scopus 로고
    • Interpolation error-based a posteriori error estimation for two-point boundary value problems and parabolic equations in one space dimension
    • P. K. Moore, Interpolation error-based a posteriori error estimation for two-point boundary value problems and parabolic equations in one space dimension. Numer. Math. (2001) 90, 149-177.
    • (2001) Numer. Math. , vol.90 , pp. 149-177
    • Moore, P.K.1
  • 14
    • 0141575485 scopus 로고    scopus 로고
    • Applications of Lobatto polynomials to an adaptive finite element method: A posteriori error estimates for hp-adaptivity and grid-to-grid interpolation
    • P. K. Moore, Applications of Lobatto polynomials to an adaptive finite element method: a posteriori error estimates for hp-adaptivity and grid-to-grid interpolation. Numer. Math. (2003) 94, 367-401.
    • (2003) Numer. Math. , vol.94 , pp. 367-401
    • Moore, P.K.1
  • 15
    • 0141514387 scopus 로고    scopus 로고
    • Implicit interpolation error-based error estimation for reaction-diffusion equations in two space dimensions
    • P. K. Moore, Implicit interpolation error-based error estimation for reaction-diffusion equations in two space dimensions. Comp. Meth. Appl. Mech. Engrg. (2003) 192, 4379-4401.
    • (2003) Comp. Meth. Appl. Mech. Engrg. , vol.192 , pp. 4379-4401
    • Moore, P.K.1
  • 16
    • 0346973360 scopus 로고    scopus 로고
    • Interpolation error-based a posteriori error estimation for hp-refinement using first and second derivative jumps
    • P. K. Moore, Interpolation error-based a posteriori error estimation for hp-refinement using first and second derivative jumps. Appl. Numer. Math. (2004) 48, 63-82.
    • (2004) Appl. Numer. Math. , vol.48 , pp. 63-82
    • Moore, P.K.1
  • 17
    • 2942613145 scopus 로고    scopus 로고
    • Implicit interpolation error-based error estimation for semilinear elliptic and parabolic equations in two space dimensions
    • P. K. Moore, Implicit interpolation error-based error estimation for semilinear elliptic and parabolic equations in two space dimensions. SMU Tech. Report No. 2002-05.
    • SMU Tech. Report No. 2002-05 , vol.2002 , Issue.5
    • Moore, P.K.1
  • 19
    • 0033413802 scopus 로고    scopus 로고
    • A posteriori error estimation with the finite element method of lines for a nonlinear parabolic equation in one space dimension
    • K. Segeth, A posteriori error estimation with the finite element method of lines for a nonlinear parabolic equation in one space dimension. Numer. Math. (1999) 83, 455-475.
    • (1999) Numer. Math. , vol.83 , pp. 455-475
    • Segeth, K.1
  • 21
    • 0022047609 scopus 로고
    • Mesh design for the p-version of the finite element method
    • B. Szabo, Mesh design for the p-version of the finite element method. Comp. Meth. Appl. Mech. Engrg. (1986) 55, 181-197.
    • (1986) Comp. Meth. Appl. Mech. Engrg. , vol.55 , pp. 181-197
    • Szabo, B.1
  • 24
    • 0001791399 scopus 로고
    • Asymptotically exact a-posteriori error estimator for elements of bi-even degree
    • D. Yu, Asymptotically exact a-posteriori error estimator for elements of bi-even degree. Math. Numerica Sinica (1991) 19, 89-101.
    • (1991) Math. Numerica Sinica , vol.19 , pp. 89-101
    • Yu, D.1
  • 25
    • 0000989710 scopus 로고
    • Asymptotically exact a-posteriori error estimator for elements of bi-odd degree
    • D. Yu, Asymptotically exact a-posteriori error estimator for elements of bi-odd degree. Math. Numerica Sinica (1991) 19, 307-314.
    • (1991) Math. Numerica Sinica , vol.19 , pp. 307-314
    • Yu, D.1
  • 27
    • 0032687062 scopus 로고    scopus 로고
    • The relationship of some a posteriori error estimators
    • J. Z. Zhu and Z. Zhang, The relationship of some a posteriori error estimators. Comp. Meth. Appl. Mech. Engng. (1999) 176, 463-475.
    • (1999) Comp. Meth. Appl. Mech. Engng. , vol.176 , pp. 463-475
    • Zhu, J.Z.1    Zhang, Z.2
  • 28
    • 0026866050 scopus 로고
    • The superconvergence patch recovery and a posteriori error estimates, Part 1. The recovery technique
    • O. C. Zienkiewicz and J. Z. Zhu, The superconvergence patch recovery and a posteriori error estimates, Part 1. The recovery technique. Int. J. Numer. Math. Engrg. (1992) 33, 1331-1364.
    • (1992) Int. J. Numer. Math. Engrg. , vol.33 , pp. 1331-1364
    • Zienkiewicz, O.C.1    Zhu, J.Z.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.