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Volumn 45, Issue 2, 2007, Pages 457-472

Optimal convergence for the implicit space-time discretization of parabolic systems with p-structure

Author keywords

Degenerate parabolic system; Error analysis; Finite element methods; Time discretization; Weak and strong solution

Indexed keywords

BOUNDARY CONDITIONS; EULER EQUATIONS; FINITE ELEMENT METHOD;

EID: 34547530180     PISSN: 00361429     EISSN: None     Source Type: Journal    
DOI: 10.1137/05064120X     Document Type: Article
Times cited : (71)

References (25)
  • 2
    • 42649142386 scopus 로고    scopus 로고
    • J. W. BARRETT AND W. B. LIU, Finite element approximation of some degenerate quasilinear elliptic and parabolic problems, in Numerical Analysis 1993, Pitman Res. Notes Math. Ser. 303, Longman Scientific and Technical, Harlow, UK, 1994, pp. 1-16.
    • J. W. BARRETT AND W. B. LIU, Finite element approximation of some degenerate quasilinear elliptic and parabolic problems, in Numerical Analysis 1993, Pitman Res. Notes Math. Ser. 303, Longman Scientific and Technical, Harlow, UK, 1994, pp. 1-16.
  • 3
    • 0028413859 scopus 로고
    • Finite element approximation of the parabolic p-Laplacian
    • J. W. BARRETT AND W. B. LIU, Finite element approximation of the parabolic p-Laplacian, SIAM J. Numer. Anal., 31 (1994), pp. 413-428.
    • (1994) SIAM J. Numer. Anal , vol.31 , pp. 413-428
    • BARRETT, J.W.1    LIU, W.B.2
  • 4
    • 0000898818 scopus 로고
    • Finite element error estimates for nonlinear elliptic equations of monitone type
    • S. S. CHOW, Finite element error estimates for nonlinear elliptic equations of monitone type, Numer. Math., 54 (1988), pp. 373-393.
    • (1988) Numer. Math , vol.54 , pp. 373-393
    • CHOW, S.S.1
  • 7
    • 42649124416 scopus 로고    scopus 로고
    • L. DIENING, A. PROHL, AND M. RŮŽ IČKA, On time-discretizations for generalized Newtonian fluids, in Nonlinear Problems in Mathematical Physics and Related Topics, II. Int. Math. Ser. (N.Y.) 2, Kluwer Academic Publishers, New York, 2002, pp. 89-118.
    • L. DIENING, A. PROHL, AND M. RŮŽ IČKA, On time-discretizations for generalized Newtonian fluids, in Nonlinear Problems in Mathematical Physics and Related Topics, II. Int. Math. Ser. (N.Y.) 2, Kluwer Academic Publishers, New York, 2002, pp. 89-118.
  • 8
    • 23944484056 scopus 로고    scopus 로고
    • Strong solutions for generalized Newtonian fluids
    • L. DIENING AND M. RŮŽČKA, Strong solutions for generalized Newtonian fluids, J. Math. Fluid Mech., 7 (2005), pp. 413-450.
    • (2005) J. Math. Fluid Mech , vol.7 , pp. 413-450
    • DIENING, L.1    RŮŽČKA, M.2
  • 10
    • 17444422552 scopus 로고    scopus 로고
    • Quasi-norm interpolation error estimates for the piecewise linear finite element approximation of p-Laplacian problems
    • C. EBMEYER AND W. B. LIU, Quasi-norm interpolation error estimates for the piecewise linear finite element approximation of p-Laplacian problems, Numer. Math., 100 (2005), pp. 233-258.
    • (2005) Numer. Math , vol.100 , pp. 233-258
    • EBMEYER, C.1    LIU, W.B.2
  • 11
    • 27144552272 scopus 로고    scopus 로고
    • Global regularity in fractional order Sobolev spaces for the p-Laplace equation on polyhedral domains
    • C. EBMEYER, W. B. LIU, AND M. STEINHAUER, Global regularity in fractional order Sobolev spaces for the p-Laplace equation on polyhedral domains, Z. Anal. Anwendungen, 24 (2005), pp. 353-374.
    • (2005) Z. Anal. Anwendungen , vol.24 , pp. 353-374
    • EBMEYER, C.1    LIU, W.B.2    STEINHAUER, M.3
  • 12
    • 33748431413 scopus 로고    scopus 로고
    • Regularity in Sobolev spaces of steady flows of fluids with shear-dependent viscosity
    • C. EBMEYER, Regularity in Sobolev spaces of steady flows of fluids with shear-dependent viscosity, Math. Methods Appl. Sci., 29 (2006), pp. 1687-1707.
    • (2006) Math. Methods Appl. Sci , vol.29 , pp. 1687-1707
    • EBMEYER, C.1
  • 13
    • 0032395606 scopus 로고    scopus 로고
    • A mixed finite element method for a nonlinear Dirichlet problem
    • M. FARHLOUL, A mixed finite element method for a nonlinear Dirichlet problem, IMA J. Numer. Anal., 18 (1998), pp. 121-132.
    • (1998) IMA J. Numer. Anal , vol.18 , pp. 121-132
    • FARHLOUL, M.1
  • 16
    • 0016536442 scopus 로고
    • Sur l'approximation, par éléments finis d'ordre un, et la résolution, par pénalisation-dualité, d'une class problèmes de Dirichlet non linéaires
    • R. GLOWINSKI AND A. MARROCCO, Sur l'approximation, par éléments finis d'ordre un, et la résolution, par pénalisation-dualité, d'une class problèmes de Dirichlet non linéaires, RAIRO Anal. Numér., 9 (1975), pp. 41-76.
    • (1975) RAIRO Anal. Numér , vol.9 , pp. 41-76
    • GLOWINSKI, R.1    MARROCCO, A.2
  • 19
    • 0035734315 scopus 로고    scopus 로고
    • Quasi-norm local error estimates for p-Laplacian
    • W. LIU AND N. YAN, Quasi-norm local error estimates for p-Laplacian, SIAM J. Numer. Anal., 39 (2001), pp. 100-127.
    • (2001) SIAM J. Numer. Anal , vol.39 , pp. 100-127
    • LIU, W.1    YAN, N.2
  • 20
    • 0035735113 scopus 로고    scopus 로고
    • On fully implicit space-time discretization for motions of incompressible fluids with shear-dependent viscosities: The case p ≤ 2
    • A. PROHL AND M. RŮŽIČKA, On fully implicit space-time discretization for motions of incompressible fluids with shear-dependent viscosities: The case p ≤ 2, SIAM J. Numer. Anal., 39 (2001), pp. 214-249.
    • (2001) SIAM J. Numer. Anal , vol.39 , pp. 214-249
    • PROHL, A.1    RŮŽIČKA, M.2
  • 21
    • 0001779231 scopus 로고    scopus 로고
    • Error analysis for implicit approximations to solutions to Cauchy problems
    • J. RULLA, Error analysis for implicit approximations to solutions to Cauchy problems, SIAM J. Numer. Anal., 33 (1996), pp. 68-87.
    • (1996) SIAM J. Numer. Anal , vol.33 , pp. 68-87
    • RULLA, J.1
  • 22
    • 84867942052 scopus 로고    scopus 로고
    • Modeling, mathematical, and numerical analysis of electrorheological fluids
    • M. RŮŽIČKA, Modeling, mathematical, and numerical analysis of electrorheological fluids, Appl. Math., 49 (2004), pp. 565-609.
    • (2004) Appl. Math , vol.49 , pp. 565-609
    • RŮŽIČKA, M.1
  • 23
    • 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
    • 0003345958 scopus 로고    scopus 로고
    • Galerkin Finite Element Methods for Parabolic Problems
    • Springer-Verlag, Berlin
    • V. THOMÉE, Galerkin Finite Element Methods for Parabolic Problems, Springer Ser. Comput. Math. 25, Springer-Verlag, Berlin, 1997.
    • (1997) Springer Ser. Comput. Math , vol.25
    • THOMÉE, V.1
  • 25
    • 0026841004 scopus 로고
    • Existence, uniqueness, and numerical analysis of solutions of a quasilinear parabolic problem
    • D. WEI, Existence, uniqueness, and numerical analysis of solutions of a quasilinear parabolic problem, SIAM J. Numer. Anal., 29 (1992), pp. 484-497.
    • (1992) SIAM J. Numer. Anal , vol.29 , pp. 484-497
    • WEI, D.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.