Adaptive approximate globally convergent algorithm with backscattered data.
Paper i proceeding, 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.

Författare

Mohammad Asadzadeh

Göteborgs universitet

Chalmers, Matematiska vetenskaper, Matematik

Larisa Beilina

Göteborgs universitet

Chalmers, Matematiska vetenskaper, Matematik

Springer Proceedings in Mathematics and Statistics

21941009 (ISSN) 21941017 (eISSN)

Vol. 52 1-20
978-3-319-00659-8 (ISBN)

Ämneskategorier

Matematik

Fundament

Grundläggande vetenskaper

DOI

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

ISBN

978-3-319-00659-8

Mer information

Senast uppdaterat

2024-01-03