A modified quasi-boundary value method for a two-dimensional inverse heat conduction problem

Abstract

In this study, we consider a two-dimensional inverse heat conduction problem, which determines the surface temperature and heat flux distribution from measured data at the fixed location. The problem is seriously ill posed in the Hadamard sense and a conditional stability is given for it. We propose a modified quasi-boundary value regularization method to deal with the ill-posed problem. By choosing suitable regularization parameters and introducing some technical inequalities, we obtain quite sharp error estimates between the approximate solution and its exact solution.