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Volumn 29, Issue 4, 2009, Pages 917-936

Convergence rates for adaptive finite elements

Author keywords

Adaptive finite elements; Convergence rates; Optimality; Regularity

Indexed keywords

ADAPTIVE FINITE ELEMENT; ADAPTIVE FINITE ELEMENT METHODS; CONVERGENCE RATES; LAGRANGE FINITE ELEMENTS; OPTIMALITY; POLYNOMIAL DEGREE; REGULARITY; SINGULAR PARTS;

EID: 71049131730     PISSN: 02724979     EISSN: 14643642     Source Type: Journal    
DOI: 10.1093/imanum/drn039     Document Type: Article
Times cited : (45)

References (24)
  • 1
    • 0029755025 scopus 로고    scopus 로고
    • Graded mesh refinement and error estimates for finite element solutions of elliptic boundary value problems in non-smooth domains
    • APEL, T., SäNDIG, A.-M. & WHITEMAN, J. R. (1996) Graded mesh refinement and error estimates for finite element solutions of elliptic boundary value problems in non-smooth domains. Math. Methods Appl. Sci., 19, 63-85.
    • (1996) Math. Methods Appl. Sci. , vol.19 , pp. 63-85
    • Apel, T.1    Sändig, A.-M.2    Whiteman, J.R.3
  • 3
    • 0001772076 scopus 로고
    • Feedback and adaptive finite element solution of one-dimensional boundary value problems
    • BABUSKA, I. & VOGELIUS, M. (1984) Feedback and adaptive finite element solution of one-dimensional boundary value problems. Numer. Math., 44, 75-102.
    • (1984) Numer. Math. , vol.44 , pp. 75-102
    • Babuska, I.1    Vogelius, M.2
  • 4
    • 2442452617 scopus 로고    scopus 로고
    • Adaptive finite element methods with convergence rates
    • BINEV, P., DAHMEN, W. & DEVORE, R. (2004) Adaptive finite element methods with convergence rates. Numer. Math., 97, 219-268.
    • (2004) Numer. Math. , vol.97 , pp. 219-268
    • Binev, P.1    Dahmen, W.2    Devore, R.3
  • 6
  • 8
    • 0002494590 scopus 로고    scopus 로고
    • Besov regularity for elliptic boundary value problems
    • DAHLKE, S. & DEVORE, R. (1997) Besov regularity for elliptic boundary value problems. Commun. Partial Differ. Equ., 22, 11-16.
    • (1997) Commun. Partial Differ. Equ. , vol.22 , pp. 11-16
    • Dahlke, S.1    Devore, R.2
  • 9
    • 0003074690 scopus 로고
    • Elliptic Boundary Value Problems on Corner Domains
    • Berlin: Springer
    • DAUGE, M. (1988) Elliptic Boundary Value Problems on Corner Domains. Lecture Notes in Mathematics, vol.1341. Berlin: Springer.
    • (1988) Lecture Notes in Mathematics , vol.1341
    • Dauge, M.1
  • 10
    • 1542639888 scopus 로고    scopus 로고
    • A convergent adaptive algorithm for Poisson's equation
    • DÖRFLER, W. (1996) A convergent adaptive algorithm for Poisson's equation. SIAM J. Numer. Anal., 33, 1106-1124.
    • (1996) SIAM J. Numer. Anal. , vol.33 , pp. 1106-1124
    • Dörfler, W.1
  • 13
    • 0016380845 scopus 로고
    • On the Poisson equation with intersecting interfaces
    • KELLOGG, R. B. (1975) On the Poisson equation with intersecting interfaces. Appl. Anal., 4, 101-129.
    • (1975) Appl. Anal. , vol.4 , pp. 101-129
    • Kellogg, R.B.1
  • 14
    • 4244208596 scopus 로고
    • Technical Note BN-1137. College Park, MD: Institute for Physical Science and Technology, University of Maryland
    • KELLOGG, R. B. (1992) Notes on piecewise smooth elliptic boundary value problems. Technical Note BN-1137. College Park, MD: Institute for Physical Science and Technology, University of Maryland.
    • (1992) Notes on Piecewise Smooth Elliptic Boundary Value Problems
    • Kellogg, R.B.1
  • 15
    • 0038271905 scopus 로고    scopus 로고
    • Local a posteriori error estimates and adaptive control of pollution effects
    • LIAO, X. & NOCHETTO, R. H. (2003) Local a posteriori error estimates and adaptive control of pollution effects. Numer. Methods Partial Differ. Equ., 19, 421-442.
    • (2003) Numer. Methods Partial Differ. Equ. , vol.19 , pp. 421-442
    • Liao, X.1    Nochetto, R.H.2
  • 16
    • 33644998367 scopus 로고    scopus 로고
    • Convergence of adaptive finite element methods for general second order linear elliptic PDE
    • MEKCHAY, K. & NOCHETTO, R. H. (2005) Convergence of adaptive finite element methods for general second order linear elliptic PDE. SIAM J. Numer. Anal., 43, 1803-1827.
    • (2005) SIAM J. Numer. Anal. , vol.43 , pp. 1803-1827
    • Mekchay, K.1    Nochetto, R.H.2
  • 17
    • 0036959161 scopus 로고    scopus 로고
    • Convergence of adaptive finite element methods
    • MORIN, P., NOCHETTO, R. H. & SIEBERT, K. G. (2002) Convergence of adaptive finite element methods. SIAM Rev., 44, 631-658.
    • (2002) SIAM Rev. , vol.44 , pp. 631-658
    • Morin, P.1    Nochetto, R.H.2    Siebert, K.G.3
  • 18
    • 44349193375 scopus 로고    scopus 로고
    • A basic convergence result for conforming adaptive finite element methods
    • MORIN, P., SIEBERT, K. G. & VEESER, A. (2007) A basic convergence result for conforming adaptive finite element methods. Math. Models Methods Appl. Sci., 18, 707-737.
    • (2007) Math. Models Methods Appl. Sci. , vol.18 , pp. 707-737
    • Morin, P.1    Siebert, K.G.2    Veeser, A.3
  • 19
    • 84966202728 scopus 로고
    • An adaptive finite element method for the two-phase Stefan problems in two space dimensions. Part I: Stability and error estimates
    • NOCHETTO, R. H., PAOLINI, M. & VERDI, C. (1991) An adaptive finite element method for the two-phase Stefan problems in two space dimensions. Part I: stability and error estimates. Math. Comput., 57, 73-108;
    • (1991) Math. Comput. , vol.57 , pp. 73-108
    • Nochetto, R.H.1    Paolini, M.2    Verdi, C.3
  • 21
    • 58849119533 scopus 로고    scopus 로고
    • A safeguarded dual weighted residual method
    • doi:10.1093/imanum/drm026
    • NOCHETTO, R. H., VEESER, A. & VERANI, M. (2008) A safeguarded dual weighted residual method. IMA J. Numer. Anal., doi:10.1093/imanum/drm026.
    • (2008) IMA J. Numer. Anal.
    • Nochetto, R.H.1    Veeser, A.2    Verani, M.3
  • 23
    • 34250183086 scopus 로고    scopus 로고
    • Optimality of a standard adaptive finite element method
    • STEVENSON, R. (2007) Optimality of a standard adaptive finite element method. Found. Comput. Math., 7, 245-269.
    • (2007) Found. Comput. Math. , vol.7 , pp. 245-269
    • Stevenson, R.1
  • 24
    • 38849110048 scopus 로고    scopus 로고
    • The completion of locally refined simplicial partitions created by bisection
    • STEVENSON, R. (2008) The completion of locally refined simplicial partitions created by bisection. Math. Comput., 77, 227-241.
    • (2008) Math. Comput. , vol.77 , pp. 227-241
    • Stevenson, R.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.