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Regularisation and discretisation for the inverse conductivity problem

Banff International Research Station for Mathematical Innovation and Discovery

"We review the variational approach to the inverse conductivity problem, in the case of discontinuous conductivities. We discuss several difficulties that arise, in particular instability. We present a variational approach that combines, simultaneously, regularisation and discretisation of the inverse problem. We show that the corresponding discrete regularised solutions are a good approximation of the solution to the inverse problem. The method provides a clear indication on the regularisation parameter and on the mesh size of the discretisation that should be used when solving numerically the inverse problem."

Mathematics; Partial differential equations; Global analysis, analysis on manifolds

video/mp4

Author affiliation: Università degli Studi di Trieste

2017-01-26

Attribution-NonCommercial-NoDerivatives 4.0 International

http://hdl.handle.net/2429/59855

Unreviewed

http://creativecommons.org/licenses/by-nc-nd/4.0/