The treatment of an inverse problem on a perforated domain is complicated heavily by the presence of the perforations or holes. We present several theoretical results that provide relationships between the problem on the perforated domain and the same problem on the corresponding unperforated/solid domain. The results establish that we can approximate the solution of the inverse problem on the perforated domain by instead solving the inverse problem on the associated solid domain. Examples are provided.

Computational aspects of solving inverse problems for elliptic PDEs on perforated domains using the collage method / H. Kunze, D. La Torre - In: Mathematical and computational approaches in advancing modern science and engineering / [a cura di] J. Bélair, I.A. Frigaard, H. Kunze, R. Makarov, R. Melnik, R.J. Spiteri. - [s.l] : Springer, 2016. - ISBN 9783319303796. - pp. 113-120 [10.1007/978-3-319-30379-6]

Computational aspects of solving inverse problems for elliptic PDEs on perforated domains using the collage method

D. La Torre
2016

Abstract

The treatment of an inverse problem on a perforated domain is complicated heavily by the presence of the perforations or holes. We present several theoretical results that provide relationships between the problem on the perforated domain and the same problem on the corresponding unperforated/solid domain. The results establish that we can approximate the solution of the inverse problem on the perforated domain by instead solving the inverse problem on the associated solid domain. Examples are provided.
Settore SECS-S/06 - Metodi mat. dell'economia e Scienze Attuariali e Finanziarie
Settore MAT/05 - Analisi Matematica
2016
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/2434/430097
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