English

The "exterior approach" applied to the inverse obstacle problem for the heat equation

Analysis of PDEs 2022-07-19 v1 Optimization and Control

Abstract

In this paper we consider the " exterior approach " to solve the inverse obstacle problem for the heat equation. This iterated approach is based on a quasi-reversibility method to compute the solution from the Cauchy data while a simple level set method is used to characterize the obstacle. We present several mixed formulations of quasi-reversibility that enable us to use some classical conforming finite elements. Among these, an iterated formulation that takes the noisy Cauchy data into account in a weak way is selected to serve in some numerical experiments and show the feasibility of our strategy of identification.

Keywords

Cite

@article{arxiv.1609.05682,
  title  = {The "exterior approach" applied to the inverse obstacle problem for the heat equation},
  author = {Laurent Bourgeois and Jérémi Dardé},
  journal= {arXiv preprint arXiv:1609.05682},
  year   = {2022}
}