I am trying to learn how to solve numerically the inverse problem of the heat equation ,at the beginning i want to start with the stationary eqaution :
$-div(K\nabla u)= f $ on $ \Omega $
$u=0 $ on $\partial\Omega $
I want to go through the computation method of the adjoint equation by the Lagrangian
do you know a book that gives enough details on this ? or even on another equation but with enough details in the algorithm
thank you in advance