On the numerical evaluation of fractional Sobolev norms
Carsten Burstedde - Institute for Computational Engineering and Sciences, The University of Texas at Austin, 1 University Station, C0200, Austin, TX 78712, United States (email)
In several important and active fields of modern applied
mathematics, such as the numerical solution of PDE-constrained
control problems or various applications in image processing and
data fitting, the evaluation of (integer and real) Sobolev norms
constitutes a crucial ingredient. Different approaches exist for
varying ranges of smoothness indices and with varying properties
concerning exactness, equivalence and the computing time for the
numerical evaluation. These can usually be expressed in terms of
discrete Riesz operators.
Keywords: Fractional Sobolev norm, elliptic PDE, control
problem, finite elements, biorthogonal wavelets.
Received: February 2006; Revised: February 2007; Published: June 2007.
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