Adaptive approximate globally convergent algorithm with backscattered data.
Paper in proceedings, 2013

We construct, analyze and implement an approximately globally convergent finite element scheme for a hyperbolic coefficient inverse problem in the case of backscattering data. This extends the computational aspects introduced in Asadzadeh and Beilina (Inv. Probl. 26, 115007, 2010), where using Laplace transformation, the continuous problem is reduced to a nonlinear elliptic equation with a gradient dependent nonlinearity. We investigate the behavior of the nonlinear term and discuss the stability issues as well as optimal a posteriori error bounds, based on an adaptive procedure and due to the maximal available regularity of the exact solution. Numerical implementations justify the efficiency of adaptive a posteriori approach in the globally convergent setting.

Author

Mohammad Asadzadeh

University of Gothenburg

Chalmers, Mathematical Sciences, Mathematics

Larisa Beilina

University of Gothenburg

Chalmers, Mathematical Sciences, Mathematics

Inverse Problems and Large-Scale Computations. Springer Proceedings in Mathematics and Statistics. Larisa Beilina, Yury V. Shestopalov (Eds.)

2194-1017 (eISSN)

Vol. 52 1-20

Subject Categories

Mathematics

Roots

Basic sciences

DOI

10.1007/978-3-319-00660-4_1

ISBN

978-3-319-00659-8

More information

Created

10/7/2017