  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.
