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Volumn 18, Issue 1, 2007, Pages 260-289

A unilaterally constrained quadratic minimization with adaptive finite elements

Author keywords

A posteriori error estimates; Adaptive finite elements; Conforming methods; Contact problems; Convergence of adaptive algorithms; Full contact; Obstacle problems; Optimal convergence rate; Thin obstacles; Unilaterally constrained minimization

Indexed keywords

ADAPTIVE ALGORITHMS; APPROXIMATION THEORY; CONSTRAINED OPTIMIZATION; CONVERGENCE OF NUMERICAL METHODS; FINITE ELEMENT METHOD; PROBLEM SOLVING;

EID: 39449115451     PISSN: 10526234     EISSN: None     Source Type: Journal    
DOI: 10.1137/05064597X     Document Type: Article
Times cited : (42)

References (26)
  • 3
    • 0012733866 scopus 로고    scopus 로고
    • An adaptive Uzawa FEM for the Stokes problem: Convergence without the inf-sup condition
    • E. BÄNSCH, P. MORIN, AND R. H. NOCHETTO, An adaptive Uzawa FEM for the Stokes problem: Convergence without the inf-sup condition, SIAM J. Numer. Anal., 40 (2002), pp. 1207-1229.
    • (2002) SIAM J. Numer. Anal , vol.40 , pp. 1207-1229
    • BÄNSCH, E.1    MORIN, P.2    NOCHETTO, R.H.3
  • 4
    • 11144295563 scopus 로고    scopus 로고
    • Averaging techniques yield reliable a posteriori finite element error control for obstacle problems
    • S. BARTELS AND C. CARSTENSEN, Averaging techniques yield reliable a posteriori finite element error control for obstacle problems, Numer. Math., 99 (2004), pp. 225-249.
    • (2004) Numer. Math , vol.99 , pp. 225-249
    • BARTELS, S.1    CARSTENSEN, C.2
  • 5
    • 2442452617 scopus 로고    scopus 로고
    • Adaptive finite element methods with convergence rates
    • P. BINEV, W. DAHMEN, AND R. DEVORE, Adaptive finite element methods with convergence rates, Numer. Math., 97 (2004), pp. 219-268.
    • (2004) Numer. Math , vol.97 , pp. 219-268
    • BINEV, P.1    DAHMEN, W.2    DEVORE, R.3
  • 6
    • 0002276608 scopus 로고
    • Convergence of the discrete free boundaries for finite element approximations
    • F. BREZZI AND L. A. CAFFARELLI, Convergence of the discrete free boundaries for finite element approximations, RAIRO Anal. Numér., 17 (1983), pp. 385-395.
    • (1983) RAIRO Anal. Numér , vol.17 , pp. 385-395
    • BREZZI, F.1    CAFFARELLI, L.A.2
  • 7
    • 8544220284 scopus 로고
    • Basic error estimates for elliptic problems
    • P. G. Ciarlet and J.-L. Lions, eds, North-Holland, Amsterdam
    • P. G. CIARLET, Basic error estimates for elliptic problems, in Handbook of Numerical Analysis, Vol. II, P. G. Ciarlet and J.-L. Lions, eds., North-Holland, Amsterdam, 1991, pp. 17-352.
    • (1991) Handbook of Numerical Analysis , vol.2 , pp. 17-352
    • CIARLET, P.G.1
  • 8
    • 0034356805 scopus 로고    scopus 로고
    • Adaptive wavelet methods for saddle point problems
    • S. DAHLKE, R. HOCHMUTH, AND K. URBAN, Adaptive wavelet methods for saddle point problems, M2AN Math. Model. Numer. Anal., 34 (2000), pp. 1003-1022.
    • (2000) M2AN Math. Model. Numer. Anal , vol.34 , pp. 1003-1022
    • DAHLKE, S.1    HOCHMUTH, R.2    URBAN, K.3
  • 9
    • 1542639888 scopus 로고    scopus 로고
    • A convergent adaptive algorithm for Poisson's equation
    • W. DÖRFLER, A convergent adaptive algorithm for Poisson's equation, SIAM J. Numer. Anal., 33 (1996), pp. 1106-1124.
    • (1996) SIAM J. Numer. Anal , vol.33 , pp. 1106-1124
    • DÖRFLER, W.1
  • 10
    • 0019386979 scopus 로고
    • On the finite element approximation of an elliptic variational inequality arising from an implicit time discretization of the Stefan problem
    • C. M. ELLIOTT, On the finite element approximation of an elliptic variational inequality arising from an implicit time discretization of the Stefan problem, IMA J. Numer. Anal., 1 (1981), pp. 115-125.
    • (1981) IMA J. Numer. Anal , vol.1 , pp. 115-125
    • ELLIOTT, C.M.1
  • 11
    • 11044237512 scopus 로고    scopus 로고
    • A posteriori error estimators for regularized total variation of characteristic functions
    • F. FIERRO AND A. VEESER, A posteriori error estimators for regularized total variation of characteristic functions, SIAM J. Numer. Anal., 41 (2003), pp. 2032-2055.
    • (2003) SIAM J. Numer. Anal , vol.41 , pp. 2032-2055
    • FIERRO, F.1    VEESER, A.2
  • 13
    • 0030128859 scopus 로고    scopus 로고
    • A posteriori error estimates for elliptic variational inequalities
    • R. KORNHUBER, A posteriori error estimates for elliptic variational inequalities, Comput. Math. Appl., 31 (1996), pp. 49-60.
    • (1996) Comput. Math. Appl , vol.31 , pp. 49-60
    • KORNHUBER, R.1
  • 14
    • 39449128526 scopus 로고    scopus 로고
    • R. KORNHUBER, Adaptive Monotone Multigrid Methods for Nonlinear Variational Problems, Adv. Numer. Math., B. G. Teubner, Stuttgart, 1997.
    • R. KORNHUBER, Adaptive Monotone Multigrid Methods for Nonlinear Variational Problems, Adv. Numer. Math., B. G. Teubner, Stuttgart, 1997.
  • 15
    • 0034447334 scopus 로고    scopus 로고
    • Data oscillation and convergence of adaptive FEM
    • P. MORIN, R. H. NOCHETTO, AND K. G. SIEBERT, Data oscillation and convergence of adaptive FEM, SIAM J. Numer. Anal., 38 (2000), pp. 466-488.
    • (2000) SIAM J. Numer. Anal , vol.38 , pp. 466-488
    • MORIN, P.1    NOCHETTO, R.H.2    SIEBERT, K.G.3
  • 16
    • 0036959161 scopus 로고    scopus 로고
    • Convergence of adaptive finite element methods
    • P. MORIN, R. H. NOCHETTO, AND K. G. SIEBERT, Convergence of adaptive finite element methods, SIAM Rev., 44 (2002), pp. 631-658.
    • (2002) SIAM Rev , vol.44 , pp. 631-658
    • MORIN, P.1    NOCHETTO, R.H.2    SIEBERT, K.G.3
  • 17
    • 0038129722 scopus 로고    scopus 로고
    • Local problems on stars: A posteriori error estimators, convergence, and performance
    • P. MORIN, R. H. NOCHETTO, AND K. G. SIEBERT, Local problems on stars: A posteriori error estimators, convergence, and performance, Math. Comp., 72 (2003), pp. 1067-1097.
    • (2003) Math. Comp , vol.72 , pp. 1067-1097
    • MORIN, P.1    NOCHETTO, R.H.2    SIEBERT, K.G.3
  • 18
    • 0041411640 scopus 로고    scopus 로고
    • Pointwise a posteriori error control for elliptic obstacle problems
    • R. H. NOCHETTO, K. G. SIEBERT, AND A. VEESER, Pointwise a posteriori error control for elliptic obstacle problems, Numer. Math., 95 (2003), pp. 163-195.
    • (2003) Numer. Math , vol.95 , pp. 163-195
    • NOCHETTO, R.H.1    SIEBERT, K.G.2    VEESER, A.3
  • 19
    • 27744463727 scopus 로고    scopus 로고
    • Fully localized a posteriori error estimators and barrier sets for contact problems
    • R. H. NOCHETTO, K. G. SIEBERT, AND A. VEESER, Fully localized a posteriori error estimators and barrier sets for contact problems, SIAM J. Numer. Anal., 42 (2005), pp. 2118-2135.
    • (2005) SIAM J. Numer. Anal , vol.42 , pp. 2118-2135
    • NOCHETTO, R.H.1    SIEBERT, K.G.2    VEESER, A.3
  • 20
    • 0000781293 scopus 로고    scopus 로고
    • ALBERT-Software for scientific computations and applications
    • A. SCHMIDT AND K. G. SIEBERT, ALBERT-Software for scientific computations and applications, Acta Math. Univ. Comenian. (N.S.), 70 (2000), pp. 105-122.
    • (2000) Acta Math. Univ. Comenian. (N.S.) , vol.70 , pp. 105-122
    • SCHMIDT, A.1    SIEBERT, K.G.2
  • 22
    • 84966200902 scopus 로고
    • Finite element interpolation of nonsmooth functions satisfying boundary conditions
    • L. R. SCOTT AND S. ZHANG, Finite element interpolation of nonsmooth functions satisfying boundary conditions, Math. Comp., 54 (1990), pp. 483-493.
    • (1990) Math. Comp , vol.54 , pp. 483-493
    • SCOTT, L.R.1    ZHANG, S.2
  • 24
    • 0035733517 scopus 로고    scopus 로고
    • Efficient and reliable a posteriori error estimators for elliptic obstacle problems
    • A. VEESER, Efficient and reliable a posteriori error estimators for elliptic obstacle problems, SIAM J. Numer. Anal., 39 (2001), pp. 146-167.
    • (2001) SIAM J. Numer. Anal , vol.39 , pp. 146-167
    • VEESER, A.1
  • 25
    • 0036823525 scopus 로고    scopus 로고
    • Convergent adaptive finite elements for the nonlinear Laplacian
    • A. VEESER, Convergent adaptive finite elements for the nonlinear Laplacian, Numer. Math., 92 (2002), pp. 743-770.
    • (2002) Numer. Math , vol.92 , pp. 743-770
    • VEESER, A.1
  • 26
    • 39449094564 scopus 로고    scopus 로고
    • R. VERFÜRTH, A Review of a Posteriori Error Estimation and Adaptive Mesh-Refinement Techniques, Adv. Numer. Math., John Wiley, Chichester, UK, 1996.
    • R. VERFÜRTH, A Review of a Posteriori Error Estimation and Adaptive Mesh-Refinement Techniques, Adv. Numer. Math., John Wiley, Chichester, UK, 1996.


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.