Larisa Beilina and Michael V. Klibanov
A globally convergent numerical method and the adaptivity technique for a hyperbolic coefficient inverse problem. Part I: analytical study.
(363K, pdf)

ABSTRACT.  A globally convergent numerical method for a multidimensional Coefficient 
Inverse Problem for a hyperbolic equation is presented. It is shown that 
this technique provides a good starting point for the so-called finite 
element adaptive method (adaptivity). This leads to a natural two-stage 
numerical procedure, which synthesizes both these methods. 
A new method for obtaining a posteriori 
error estimates for the adaptivity tecxhnique is demonstrated on a specific example 
of a hyperbolic Coefficient Inverse Problem.