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

Abstract

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 Hölder-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.

Keywords

• ill-posed problem
• inverse heat conduction problem
• regularization
• a posteriori parameter choice strategy
• error estimate
• 65m30
• 35r30
• 35r25