Estimation of the diffusion coefficient by interval methods, level curves and bicubic splines
(English)Article in journal (Other academic) Submitted
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.
inverse problem, bicubic spline, interval analysis, heat equation
Research subject Mathematics
IdentifiersURN: urn:nbn:se:uu:diva-161311OAI: oai:DiVA.org:uu-161311DiVA: diva2:483515
FunderSwedish Research Council, 2005-3152