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Estimation of the diffusion coefficient by interval methods, level curves and bicubic splines
Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Analysis and Applied Mathematics. (CAPA)
(English)Article in journal (Other academic) Submitted
Abstract [en]

We propose a new method for estimating a solution dependent diffusion coefficient in the heat equation, given a numerical solution to the latter. The main idea is to use a set–valued approximation of the solution in order to construct constraints on the coefficient. These constraints enable us to obtain a cover of the graph of the diffusion coefficient for a discrete set of temperatures. We illustrate the pros and cons of our method on several examples.

Keyword [en]
inverse problem, bicubic spline, interval analysis, heat equation
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URN: urn:nbn:se:uu:diva-161311OAI: oai:DiVA.org:uu-161311DiVA: diva2:483515
Swedish Research Council, 2005-3152
Available from: 2012-01-25 Created: 2011-11-10 Last updated: 2012-03-16Bibliographically approved

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