New conception of the FEM base functions applied to solving an inverse heat transfer problem

The present work shows the modified concept of the finite element method which has been applied to the solution of the inverse problem (of Cauchy type) for heat conduction equation in a circular ring. The main idea of the new concept consists of the application a new type of base function which cause the vanishing of some integrals in the strong formulation. The calculation with the new base functions takes place in the physical space, and there is no need to go to the isoparametric one. Numerical calculations of the inverse problem confirm the good properties of a new set of base functions.