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  • 1
    Electronic Resource
    Electronic Resource
    A wavelet Galerkin method for the stokes equations (1996)
    Springer
    Computing 56 (1996), S. 259-301 
    Details
    ISSN: 1436-5057
    Keywords: 15A12 ; 35Q30 ; 65N30 ; 41A17 ; 41A63 ; Saddle point problems ; LBB condition ; multiresolution analysis ; wavelets ; time dependent problems ; Schur complements ; preconditioning
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science
    Description / Table of Contents: Zusammenfassung In dieser Arbeit werden Galerkin-Verfahren für das Stokes-Problem untersucht, die auf speziell angepaßten Multiresolution-Ansätzen beruhen. Insbesondere wird gezeigt, daß gewisse Konstruktionsprinzipien für Wavelets auf gleichförmigen Gittern für jede Raumdimension und beliebige gewünschte Exaktheitsordnung auf Parre von Ansatzräumen führen, die die Ladyšenskaja-Babuška-Brezzi-Bedingung erfüllen. Darüber hinaus ergeben sich auch im instationären Fall aus den entsprechenden stabilen Multiskalenzerlegungen effiziente Vorkonditionierer für die Schurkomplemente entsprechenden systemmatrizen. Die Ergebnisse werden anhand einiger konkreter Realisierungen und numerischer Tests illustriert.
    Notes: Abstract The purpose of this paper is to investigate Galerkin schemes for the Stokes equations based on a suitably adapted multiresolution analysis. In particular, it will be shown that techniques developed in connection with shift-invariant refinable spaces give rise to trial spaces of any desired degree of accuracy satisfying the Ladyšenskaja-Babuška-Brezzi condition for any spatial dimension. Moreover, in the time dependent case efficient preconditioners for the Schur complements of the discrete systems of equations can be based on corresponding stable multiscale decompositions. The results are illustrated by some concrete examples of adapted wavelets and corresponding numerical experiments.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02238515
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  • 2
    Electronic Resource
    Electronic Resource
    Microwave surface resistance of epitaxial YBa2Cu3O7 thin films at 18.7 GHz measured by a dielectric resonator technique (1992)
    Springer
    Journal of superconductivity 5 (1992), S. 195-201 
    Details
    ISSN: 1572-9605
    Keywords: High-temperature superconductivity ; microwave cavities ; sample surface impedance
    Source: Springer Online Journal Archives 1860-2000
    Topics: Electrical Engineering, Measurement and Control Technology , Physics
    Notes: Abstract We used a dielectric resonator technique for highly sensitive measurements of the temperature dependence of the microwave surface resistanceR s of 1×1 cm2 superconducting films at 18.7 GHz. It consists of a sapphire disc positioned on the film under investigation within a copper cavity which is acting as a radiation shield. In the TE01δ oscillation mode the highly reproducible quality factor of about 105 results in a sensitivity of ±50μΩ forR s measurements. The temperature dependence ofR s can be measured up to values as high as 1 Ω. We have investigated several YBa2Cu3O7 thin films prepared by high oxygen pressure d.c. sputtering on LaAlO3 and NdGaO3. Our best films exhibit a pronounced nonlinear behavior of the d.c. resistivityρ(T) withρ(300K)/ρ(100K) values of about 3.7. Those films show, besides the initial fall-off just belowT c , a further strong decrease ofR s at low temperatures. This was observed both at 18.7 GHz and 87 GHz, as measured by a conventional cavity end plate replacement technique. ForT≪Tc/2 these films exhibit an exp (−αT c/T) dependence ofR s withα-values around 0.4. These observations may be explained by a superconducting energy gap with 2Δ/kT c≈0.8 for charge carriers localized in the CuO chains for YBa2Cu3O7.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00618067
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    Paper (German National Licenses)
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