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  • 1
    Electronic Resource
    Electronic Resource
    First Cesaro sums for high order finite elements near singularities (1977)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 11 (1977), S. 753-755 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: High order finite elements often exhibit an oscillatory behaviour near stress singularities which appears similar to the Gibbs phenomenon in the theory of Fourier series. It is known that under certain conditions the average of successive partial sums (the first Cesaro sum) of a Fourier series exhibiting the Gibbs phenomenon will converge monotonically to the function being approximated. An analogous device introduced for high order finite element approximations near a stress singularity successfully smooths the oscillations of the computed stress.
    Additional Material: 1 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620110411
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  • 2
    Electronic Resource
    Electronic Resource
    p-convergent finite element approximations in fracture mechanics (1978)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 12 (1978), S. 551-560 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The strain energy release rate (G) converges rapidly in finite element approximations in which the finite element mesh is fixed and the order of polynomial displacement interpolations (p) is increased. Numerical experiments indicate that the error inG is very closely estimated, even for small pand very coarse finite element meshes, by an expression of the form k (NDF)-1 in which k is a mesh dependent constant and NDF is the number of degrees-of-freedom. The method provides for very efficient and accurate computation of G without the use of special techniques.
    Additional Material: 6 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620120313
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