Abstract

In this talk, we revisit a Cauchy problem of recovering both missing value and flux on inaccessible boundary from Dirichlet and Neumann data measured on the remaining accessible boundary. With an introduction of a relaxation parameter, the Dirichlet boundary conditions are approximated by two Robin ones. Compared to the existing work, weaker regularity is required on the Dirichlet data. This makes the proposed model simpler and more efficient in computation. Associated with two mixed boundary value problems, a regularized Kohn-Vogelius formulation is proposed, which leads to a regularization framework with two regularization parameters. A series of theoretical results are established for the new reconstruction model. Several numerical examples are provided to verify the feasibility of the proposed method.