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  • 2000-2004  (2)
  • 1
    Electronic Resource
    Electronic Resource
    Springer
    Calcolo 37 (2000), S. 65-77 
    ISSN: 1126-5434
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract: Adaptive mesh design based on a posteriori error control is studied for finite element discretisations for variational problems of Signorini type. The techniques to derive residual based error estimators developed, e.g., in ([2, 10, 20]) are extended to variational inequalities employing a suitable adaptation of the duality argument [17]. By use of this variational argument weighted a posteriori estimates for controlling arbitrary functionals of the error are derived here for model situations for contact problems. All arguments are based on Hilbert space methods and can be carried over to the more general situation of linear elasticity. Numerical examples demonstrate that this approach leads to effective strategies for designing economical meshes and to bounds for the error which are useful in practice.
    Type of Medium: Electronic Resource
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  • 2
    ISSN: 1365-3040
    Source: Blackwell Publishing Journal Backfiles 1879-2005
    Topics: Biology
    Notes: Photosynthesis is commonly stimulated in grasslands with experimental increases in atmospheric CO2 concentration ([CO2]), a physiological response that could significantly alter the future carbon cycle if it persists in the long term. Yet an acclimation of photosynthetic capacity suggested by theoretical models and short-term experiments could completely remove this effect of CO2. Perennial ryegrass (Lolium perenne L. cv. Bastion) was grown under an elevated [CO2] of 600 µmol mol−1 for 10 years using Free Air CO2Enrichment (FACE), with two contrasting nitrogen levels and abrupt changes in the source : sink ratio following periodic harvests. More than 3000 measurements characterized the response of leaf photosynthesis and stomatal conductance to elevated [CO2] across each growing season for the duration of the experiment. Over the 10 years as a whole, growth at elevated [CO2] resulted in a 43% higher rate of light-saturated leaf photosynthesis and a 36% increase in daily integral of leaf CO2 uptake. Photosynthetic stimulation was maintained despite a 30% decrease in stomatal conductance and significant decreases in both the apparent, maximum carboxylation velocity (Vc,max) and the maximum rate of electron transport (Jmax). Immediately prior to the periodic (every 4–8 weeks) cuts of the L. perenne stands, Vc,max and Jmax, were significantly lower in elevated than in ambient [CO2] in the low-nitrogen treatment. This difference was smaller after the cut, suggesting a dependence upon the balance between the sources and sinks for carbon. In contrast with theoretical expectations and the results of shorter duration experiments, the present results provide no significant change in photosynthetic stimulation across a 10-year period, nor greater acclimation in Vc,max and Jmax in the later years in either nitrogen treatment.
    Type of Medium: Electronic Resource
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