Numerical solution of a 2D inverse heat conduction problem

We consider a two-dimensional (2D) inverse heat conduction problem which is severely ill-posed, i.e. the solution (if it exists) does not depend continuously on the data. For obtaining a stable approximate solution, we propose an iterative regularization method from a new point of view. On the one hand, we give and prove some order optimal convergence results in the L-2-norm and H-r-norm under both apriori and a posteriori stopping rules, on the other hand, we discuss the numerical aspect of the proposed method. Three numerical examples illustrate the behaviour of the regularization method.