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

作者：Baudouin Lucie^*; Eryedoza Sylvain; Osses Axel

来源：Journal de Mathematiques Pures et Appliquees, 2015, 103(6): 1475-1522.

DOI：10.1016/j.matpur.2014.11.006

• Discrete Carleman estimates
• Inverse problem
• Stability estimates
• Wave equation

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 potential.

• 出版日期2015-6