Different finite element approaches for inverse heat conduction problems

Abstract

In this study, three different versions of the finite element method (FEM) based on Trefftz functions are presented for solving transient two-dimensional inverse heat conduction problems. The following cases are considered: (a) FEM with the condition of continuity of temperature in the common nodes of elements, (b) no temperature continuity at any point between elements and (c) nodeless FEM. Instead, in each finite element the temperature is approximated by a linear combination of Trefftz functions. These investigations are carried out using temperature data obtained from numerical simulations, exact and disturbed. For the inaccurate data some efficient method of smoothing is presented.

Keywords:

• transient heat conduction
• inverse problem
• Trefftz functions
• FEM
• energetic minimization

AMS Subject Classiffications::

• 80A23
• 80M10
• 65D10
• 78M10

Acknowledgements

This work was carried out in the framework of the research project No. N513 003 32/0541, which was financed by the resources for the development of science in the years 2007–2009.