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  • Electronic Resource  (2)
  • 1
    Electronic Resource
    Electronic Resource
    On the numerical approximation of unstable minimal surfaces with polygonal boundaries (1996)
    Springer
    Numerische Mathematik 73 (1996), S. 95-118 
    Details
    ISSN: 0945-3245
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary. This work is concerned with the approximation and the numerical computation of polygonal minimal surfaces in ${\Bbb R}^q (q \ge 2)$ . Polygonal minimal surfaces correspond to the critical points of Shiffman's function $\Theta$ . Since this function is analytic, polygonal minimal surfaces can be characterized by means of the second derivative of $\Theta$ . We present a finite element approximation of quasiminimal surfaces together with an error estimate. In this way we obtain discrete approximations $\Theta_h$ of $\Theta$ and $f_h$ of $\nabla \Theta$ . In particular we prove that the discrete functions converge uniformly on certain compact subsets. This will be the main tool for proving existence and convergence of discrete minimal surfaces in neighbourhoods of non-degenerate minimal surfaces. In the numerical part of this paper we compute numerical approximations of polygonal minimal surfaces by use of Newton's method applied to $f_h$ .
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/s002110050186
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    Paper (German National Licenses)
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  • 2
    Electronic Resource
    Electronic Resource
    Three Control Methods for Time-Dependent Fluid Flow (2000)
    Springer
    Flow, turbulence and combustion 65 (2000), S. 273-298 
    Details
    ISSN: 1573-1987
    Keywords: optimal control ; Navier–Stokes equations ; Newton method ; reduced order method ; proper orthogonal decomposition ; instantaneous control
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: Abstract We summarize some of the recent developments in the field of optimal and suboptimal control strategies for time-dependent incompressible Navier–Stokes equations. Besides the Newton method,reduced order modeling (ROM) and receding horizon control strategies are described. All approaches are applied to compute controls for the unsteady flow around a cylinder in two spatial dimensions.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1011417305739
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    Paper (German National Licenses)
    Fulltext
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