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Published in:
2018 | OriginalPaper | Chapter
Using the Collage Method to Solve Inverse Problems for Vector-Valued Variational Problems on a Perforated Domain in Reflexive Banach Spaces
Authors : Herb Kunze, Davide La Torre, Manuel Ruiz Galán
Published in: Recent Advances in Mathematical and Statistical Methods
Publisher: Springer International Publishing
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Abstract
Recent work establishes that the solution of the parameter estimation on a perforated domain can be approximated by instead solving the inverse problem on the much easier to work with associated solid domain. In this work, we consider vector-valued variational problems on a perforated domain and show that the inverse problems on the perforated and associated solid domains can be similarly connected. The approach relies on a “generalized collage theorem” built from the vector-valued Lax-Milgram Theorem in reflexive Banach spaces. The method will be demonstrated on a numerical example.