Title
Adaptive Wavelet and Frame Schemes for Elliptic and Parabolic Equations,Used
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This thesis is concerned with the application of wavelet methods to the adaptive numerical solutionof elliptic and parabolic operator equations over a polygonal domain. Driven by the insight that the construction of wavelet bases on more general domains is complicated and may pose stability problems, we analyze the option to replace the concept of wavelet bases by the more flexible concept of wavelet frames. Frames are redundant systems that still allow for stable decomposition and reconstruction of a given function. In the first part of this thesis, is shown how to construct socalled Gelfand frames on polygonal domains by a simple overlapping domain decomposition approach. Gelfand frames are able to characterize function spaces in a similar way as in the case of wavelet bases. The second part is concerned with the application of Gelfand frames to the adaptive numerical treatment of linear elliptic problems. We propose inexact versions of wellknown iterative schemes for the frame coordinate representation of the given operator equation. Both convergence and optimality of the considered methods can be proved and illustrated by numerical examples. In the third part, we consider adaptive wavelet methods for the numerical treatment of linear parabolic equations. Due to the initial value problem structure, we consider a semidiscretization in time with linearly implicit methods first. The arising sequence of elliptic operator equations is then solved adaptively with wavelet methods. It is shown how to exploit the key properties of wavelet bases to a considerable extent, e.g., in preconditioning strategies and for the convergence and complexity analysis of the overall algorithm. We finish with numerical experiments in one and two spatial dimensions.
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We ship your order within 2–3 business days for USA deliveries and 5–8 business days for international shipments. Once your package has been dispatched from our warehouse, you'll receive an email confirmation with a tracking number, allowing you to track the status of your delivery.
Returns
To facilitate a smooth return process, a Return Authorization (RA) Number is required for all returns. Returns without a valid RA number will be declined and may incur additional fees. You can request an RA number within 15 days of the original delivery date. For more details, please refer to our Return & Refund Policy page.
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Warranty
We provide a 2-year limited warranty, from the date of purchase for all our products.
If you believe you have received a defective product, or are experiencing any problems with your product, please contact us.
This warranty strictly does not cover damages that arose from negligence, misuse, wear and tear, or not in accordance with product instructions (dropping the product, etc.).
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