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  • 1
    Electronic Resource
    Electronic Resource
    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
    Keywords: AMS(MOS): Primary 65N30 ; R: G 1.8
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: 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.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01396320
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    Paper (German National Licenses)
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  • 2
    Electronic Resource
    Electronic Resource
    Superconvergence analysis of approximate boundary-flux calculations (1992)
    Springer
    Numerische Mathematik 63 (1992), S. 483-501 
    Details
    ISSN: 0945-3245
    Keywords: 65N30
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: 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.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01385871
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    Paper (German National Licenses)
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  • 3
    Electronic Resource
    Electronic Resource
    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
    Keywords: Mathematics and Statistics ; Numerical Methods
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: 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.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/num.1690070304
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    Paper (German National Licenses)
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  • 4
    Electronic Resource
    Electronic Resource
    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
    Keywords: Mathematics and Statistics ; Numerical Methods
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: 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.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/num.1690090506
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    Paper (German National Licenses)
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