A posteriori regularization method for the two-dimensional inverse heat conduction problem

In this article, we consider a two-dimensional inverse heat conduction problem that determines the surface temperature distribution from measured data at the fixed location. This problem is severely ill-posed, i.e., the solution does not depend continuously on the data. A quasi-boundary value regularization method in conjunction with the a posteriori parameter choice strategy is proposed to solve the problem. A Holder-type error estimate between the approximate solution and its exact solution is also given. The error estimate shows that the regularized solution is dependent continuously on the data.