"Stability of an inverse problem for the discrete wave equation and convergence results"

Research areas:
Year:
2015
Type of Publication:
Article
Keywords:
Discrete Carleman estimates, Inverse problem, Stability estimates, Wave equation
Authors:
  • L. Baudouin
  • S. Eryedoza
  • A. Osses
Journal:
JOURNAL DE MATHEMATIQUES PURES ET APPLIQUEES
Volume:
103
Pages:
1475-1522
ISSN:
0021-7824
Abstract:
Using uniform global Carleman estimates for semi-discrete elliptic and hyperbolic equations, we study Lipschitz and logarithmic stability for the inverse problem of recovering a potential in a semi-discrete wave equation, discretized by finite differences in a 2-d uniform mesh, from boundary or internal measurements. The discrete stability results, when compared with their continuous counterparts, include new terms depending on the discretization parameter h. From these stability results, we design a numerical method to compute convergent approximations of the continuous potentia