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Erschienen in:
2006 | OriginalPaper | Buchkapitel
Wavelet Schemes for Linear-Quadratic Elliptic Control Problems
verfasst von : Angela Kunoth
Erschienen in: Operations Research Proceedings 2005
Verlag: Springer Berlin Heidelberg
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This paper discusses the efficient numerical solution of a class of continuous optimization problems which are characterized by minimizing a tracking-type quadratic control functional subject to constraints in form of a linear elliptic partial differential equation (PDE) together with appropriate boundary conditions. For such problems, discretizations in terms of (domain-adapted biorthogonal spline-)wavelets offer several favorable properties over conventional approaches: from the evaluation of non-integer Sobolev norms in the objective functional over well-conditioned coupled linear systems of equations up to adaptive solution schemes with provable convergence and optimal convergence rates.