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  • 1
    Digitale Medien
    Digitale Medien
    Finite element error estimates for non-linear elliptic equations of monotone type (1989)
    Springer
    Numerische Mathematik 54 (1989), S. 373-393 
    Details
    ISSN: 0945-3245
    Schlagwort(e): AMS(MOS): Primary 65N30 ; R: G 1.8
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Mathematik
    Notizen: Summary In this paper we shall consider the application of the finite element method to a class of second order elliptic boundary value problems of divergence form and with gradient nonlinearity in the principal coefficient, and the derivation of error estimates for the finite element approximations. Such problems arise in many practical situations — for example, in shock-free airfoil design, seepage through coarse grained porous media, and in some glaciological problems. By making use of certain properties of the nonlinear coefficients, we shall demonstrate that the variational formulations associated with these boundary value problems are well-posed. We shall also prove that the abstract operators accompanying such problems satisfy certain continuity and monotonicity inequalities. With the aid of these inequalities and some standard results from approximation theory, we show how one may derive error estimates for the finite element approximations in the energy norm.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF01396320
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  • 2
    Digitale Medien
    Digitale Medien
    Superconvergence analysis of approximate boundary-flux calculations (1992)
    Springer
    Numerische Mathematik 63 (1992), S. 483-501 
    Details
    ISSN: 0945-3245
    Schlagwort(e): 65N30
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Mathematik
    Notizen: Summary Certain projection post-processing techniques have been proposed for computing the boundary flux for two-dimensional problems (e.g., see Carey, et al. [5]). In a series of numerical experiments on elliptic problems they observed that these post-processing formulas for approximate fluxes were almost (O(h 2)-accurate for linear triangular elements. In this paper we prove that the computed boundary flux isO(h 2 ln 1/h)-accurate in the maximum norm for the partial method of [5]. If the solutionuφH 3(Ω) then the boundary flux error isO(h 3/2) in theL 2-norm.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF01385871
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  • 3
    Digitale Medien
    Digitale Medien
    Natural and postprocessed superconvergence in semilinear problems (1991)
    New York, NY [u.a.] : Wiley-Blackwell
    Numerical Methods for Partial Differential Equations 7 (1991), S. 245-259 
    Details
    ISSN: 0749-159X
    Schlagwort(e): Mathematics and Statistics ; Numerical Methods
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik
    Notizen: Superconvergence error estimates are established for a class of semilinear problems defined by a linear elliptic operator with a nonlinear forcing term. The analysis is for rectangular biquadratic elements, and we prove superconvergence of the derivative components along associated lines through the Gauss points. Derivative postprocessing formula and formulas for integrals are also considered and similar superconvergence estimates proven.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1002/num.1690070304
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  • 4
    Digitale Medien
    Digitale Medien
    Superconvergence phenomena in nonlinear two-point boundary-value problems (1993)
    New York, NY [u.a.] : Wiley-Blackwell
    Numerical Methods for Partial Differential Equations 9 (1993), S. 561-577 
    Details
    ISSN: 0749-159X
    Schlagwort(e): Mathematics and Statistics ; Numerical Methods
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik
    Notizen: Superconvergence estimates are derived for a class of strongly nonlinear two-point boundary-value problems. The analysis considers solution and gradient superconvergence points as well as flux postprocessing formulas. Finally, the extension to parabolic problems is considered. © 1993 John Wiley & Sons, Inc.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1002/num.1690090506
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