A comparison of different regularization methods for a Cauchy problem in anisotropic heat conduction

In this paper, various regularization methods are numerically implemented using the boundary element method (BEM) in order to solve the Cauchy steady-state heat conduction problem in an anisotropic medium. The convergence and the stability of the numerical methods are investigated and compared The numerical results obtained confirm that stable numerical results can be obtained by various regularization methods, but if high accuracy is required for the temperature, or if the heat flux is also required, then care must be taken when choosing the regularization method since the numerical results are substantially, improved by choosing the appropriate method.