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Volumn 32, Issue 2, 2007, Pages 343-371

Preconditioned descent algorithms for p-Laplacian

Author keywords

Finite element approximation; Highly degenerate p Laplacian; Preconditioned steepest descent algorithms; Variational inequalities

Indexed keywords

CONVERGENCE ANALYSIS; FINITE ELEMENT DISCRETIZATION; PRECONDITIONED STEEPEST DESCENT ALGORITHMS; VARIATIONAL INEQUALITIES;

EID: 34547284308     PISSN: 08857474     EISSN: None     Source Type: Journal    
DOI: 10.1007/s10915-007-9134-z     Document Type: Article
Times cited : (59)

References (28)
  • 1
    • 0033448307 scopus 로고    scopus 로고
    • The approximation theory for the p-version finite element method and application to non-linear elliptic PDEs
    • Ainsworth, M., and Kay, D. (1999). The approximation theory for the p-version finite element method and application to non-linear elliptic PDEs. Numer. Math. 83, 351-388.
    • (1999) Numer. Math , vol.83 , pp. 351-388
    • Ainsworth, M.1    Kay, D.2
  • 2
    • 84864176236 scopus 로고    scopus 로고
    • 2 AN 25, 31-48.
    • 2 AN 25, 31-48.
  • 3
    • 0342572585 scopus 로고    scopus 로고
    • Bean's critical-state model as p → ∞ limit of an evolutionary p-Laplacian equation
    • Barrett, J. W., and Prigozhin, L. (2000). Bean's critical-state model as p → ∞ limit of an evolutionary p-Laplacian equation. J. Nonlinear Anal. 42, 977-993.
    • (2000) J. Nonlinear Anal , vol.42 , pp. 977-993
    • Barrett, J.W.1    Prigozhin, L.2
  • 4
    • 84968503817 scopus 로고
    • Finite element approximation of the p-Laplacian
    • Barrett, J. W., and Liu, W. B. (1993). Finite element approximation of the p-Laplacian. Math. Comp. 61, 523-537.
    • (1993) Math. Comp , vol.61 , pp. 523-537
    • Barrett, J.W.1    Liu, W.B.2
  • 5
    • 0013086439 scopus 로고
    • Finite element approximation of some degenerate quasi-linear problems
    • Barrett, J. W., and Liu, W. B. (1994). Finite element approximation of some degenerate quasi-linear problems. Lecture Notes Math. 303, 1-16
    • (1994) Lecture Notes Math , vol.303 , pp. 1-16
    • Barrett, J.W.1    Liu, W.B.2
  • 6
    • 21844482708 scopus 로고
    • Quasi-norm error bounds for finite element approximation of quasi-Newtonian flows
    • Barrett, J. W., and Liu, W. B. (1994). Quasi-norm error bounds for finite element approximation of quasi-Newtonian flows. Numer. Math. 68, 437-456.
    • (1994) Numer. Math , vol.68 , pp. 437-456
    • Barrett, J.W.1    Liu, W.B.2
  • 7
    • 0033710047 scopus 로고    scopus 로고
    • A multigrid algorithm for the p-Laplaican
    • Bermejo, R., and Infante, J. (2000). A multigrid algorithm for the p-Laplaican. SIAM, J. Sci. Comput. 21, 1774-1789.
    • (2000) SIAM, J. Sci. Comput , vol.21 , pp. 1774-1789
    • Bermejo, R.1    Infante, J.2
  • 8
    • 0037492025 scopus 로고    scopus 로고
    • A p-Laplacian approximation for some mass optimization problems
    • Bouchitte, G., Buttazzo, G., and De Pascale, L. (2003). A p-Laplacian approximation for some mass optimization problems. JOTA 118, 1-25.
    • (2003) JOTA , vol.118 , pp. 1-25
    • Bouchitte, G.1    Buttazzo, G.2    De Pascale, L.3
  • 10
    • 0000898818 scopus 로고
    • Finite element error estimates for non-linear elliptic equations of monitone type
    • Chow, S. S. (1988). Finite element error estimates for non-linear elliptic equations of monitone type. Numer. Math. 54, 373-393.
    • (1988) Numer. Math , vol.54 , pp. 373-393
    • Chow, S.S.1
  • 12
    • 0032395606 scopus 로고    scopus 로고
    • A mixed finite element method for a nonlinear Direchlet problem
    • Farhloul, M. (1998). A mixed finite element method for a nonlinear Direchlet problem. IMA J. Numer. Anal. 18, 121-132.
    • (1998) IMA J. Numer. Anal , vol.18 , pp. 121-132
    • Farhloul, M.1
  • 14
    • 0016536442 scopus 로고    scopus 로고
    • Glowinski, R., and Marrocco, A. (1975). Sur l'approximation, par éléments finis d'ordre un, et la résolution, par pénalisation-dualité, d'une classe de problémes de Dirichlet non linéaires (French). RAIRO Anal. Numer. 9(R-2), 41-76.
    • Glowinski, R., and Marrocco, A. (1975). Sur l'approximation, par éléments finis d'ordre un, et la résolution, par pénalisation-dualité, d'une classe de problémes de Dirichlet non linéaires (French). RAIRO Anal. Numer. 9(R-2), 41-76.
  • 15
    • 33750406207 scopus 로고    scopus 로고
    • Preconditioning higher order finite element systems by algebraic multigrid method of linear element
    • Huang, Y. Q., Shu, S., and Yu, X.-J. (2006). Preconditioning higher order finite element systems by algebraic multigrid method of linear element. J. Comput. Math. 24(5), 657-664.
    • (2006) J. Comput. Math , vol.24 , Issue.5 , pp. 657-664
    • Huang, Y.Q.1    Shu, S.2    Yu, X.-J.3
  • 16
    • 21344492410 scopus 로고
    • Higher order regularity for the solutions of some nonlinear degenerate elliptic equations
    • Liu, W. B., and Barrett, J. W. (1993). Higher order regularity for the solutions of some nonlinear degenerate elliptic equations. SIAM J. Math. Anal. 24(6), 1522-1536.
    • (1993) SIAM J. Math. Anal , vol.24 , Issue.6 , pp. 1522-1536
    • Liu, W.B.1    Barrett, J.W.2
  • 17
    • 38248999512 scopus 로고
    • A remark on the regularity of the solutions of p-Laplacian and its applications to their finite element approximation
    • Liu, W. B., and Barrett, J. W. (1993). A remark on the regularity of the solutions of p-Laplacian and its applications to their finite element approximation. J. Math. Anal. Appl. 178, 470-488.
    • (1993) J. Math. Anal. Appl , vol.178 , pp. 470-488
    • Liu, W.B.1    Barrett, J.W.2
  • 18
    • 38249003933 scopus 로고
    • A further remark on the regularity of the solutions of the p-Laplacian and its applications to their finite element approximation
    • Liu, W. B., and Barrett, J. W. (1993). A further remark on the regularity of the solutions of the p-Laplacian and its applications to their finite element approximation. J. Nonlinear. Anal. 21, 379-387.
    • (1993) J. Nonlinear. Anal , vol.21 , pp. 379-387
    • Liu, W.B.1    Barrett, J.W.2
  • 19
    • 0034397019 scopus 로고    scopus 로고
    • Degenerate quasilinear elliptic equations arising from bimaterial problems in elastic-plastic mechanics II
    • Liu, W. B. (2000). Degenerate quasilinear elliptic equations arising from bimaterial problems in elastic-plastic mechanics II. Numer. Math. 86, 491-506.
    • (2000) Numer. Math , vol.86 , pp. 491-506
    • Liu, W.B.1
  • 20
    • 0003344002 scopus 로고    scopus 로고
    • Finite element approximation of some degenerate monotone quasi-linear elliptic systems
    • Liu, W. B., and Barrett, J. W. (1996). Finite element approximation of some degenerate monotone quasi-linear elliptic systems. SIAM J. Numer. Anal. 33, 88-106.
    • (1996) SIAM J. Numer. Anal , vol.33 , pp. 88-106
    • Liu, W.B.1    Barrett, J.W.2
  • 21
    • 0035734315 scopus 로고    scopus 로고
    • Quasi-norm local error estimates for the finite element approximation of p-Laplacian
    • Liu, W. B., and Yan, N. (2001). Quasi-norm local error estimates for the finite element approximation of p-Laplacian. SIAM J. Numer. Anal. 39, 100-127.
    • (2001) SIAM J. Numer. Anal , vol.39 , pp. 100-127
    • Liu, W.B.1    Yan, N.2
  • 22
    • 84955240258 scopus 로고    scopus 로고
    • On quasi-norm interpolation error estimation and a posteriori error estimates for p-Laplacian
    • Liu, W. B., and Yan, N. (2003). On quasi-norm interpolation error estimation and a posteriori error estimates for p-Laplacian. SIAM J. Numer. Anal.
    • (2003) SIAM J. Numer. Anal
    • Liu, W.B.1    Yan, N.2
  • 23
    • 0035579348 scopus 로고    scopus 로고
    • Mixed finite element analysis of a non-linear three-fields Stokes model
    • Manouzi, H., and Farhloul, M. (2001). Mixed finite element analysis of a non-linear three-fields Stokes model. IMA J. Numer. Anal. 21, 143-164.
    • (2001) IMA J. Numer. Anal , vol.21 , pp. 143-164
    • Manouzi, H.1    Farhloul, M.2
  • 24
    • 0003654184 scopus 로고    scopus 로고
    • A posteriori error estimators for nonconforming approximation of some quasi-Newtonian flows
    • Padra, C. (1997). A posteriori error estimators for nonconforming approximation of some quasi-Newtonian flows. SIAM J. Numer. Anal. 34, 1600-1615.
    • (1997) SIAM J. Numer. Anal , vol.34 , pp. 1600-1615
    • Padra, C.1
  • 26
    • 84968521915 scopus 로고
    • A posteriori error estimates for non-linear problems
    • Verfürth, R. (1994). A posteriori error estimates for non-linear problems. Math. Comp. 62, 445-475.
    • (1994) Math. Comp , vol.62 , pp. 445-475
    • Verfürth, R.1
  • 27
    • 0000986730 scopus 로고    scopus 로고
    • Rate of convergence of some space decomposition method for linear and nonlinear elliptic problems
    • Tai, X. C., and Espedal, M. (1998). Rate of convergence of some space decomposition method for linear and nonlinear elliptic problems. SIAM J. Numer. Anal. 38, 1558-1570.
    • (1998) SIAM J. Numer. Anal , vol.38 , pp. 1558-1570
    • Tai, X.C.1    Espedal, M.2
  • 28
    • 0036003411 scopus 로고    scopus 로고
    • Global convergence of subspace correction methods for convex optimization problems
    • Tai, X. C., and Xu, J. (2002). Global convergence of subspace correction methods for convex optimization problems. Math. Comp. 74, 105-124.
    • (2002) Math. Comp , vol.74 , pp. 105-124
    • Tai, X.C.1    Xu, J.2


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