Adaptive mesh techniques based on a posteriori error estimates for an inverse Cauchy problem

摘要

We are interested by an alternating method for an inverse Cauchy problem. Our main results of this paper consists in exhibiting local error indicators, based on a posteriori analysis, with respect to both space approximation and iterative algorithms. In contrast to existing results, the choice of adaptive finite element meshes will be considered after a comparison between the two kinds of indicators. This lead to an efficient method which have the ability to dramatically reduce the computational cost comparing with uniform grid refinement. Some numerical experiments support these results.