2012/01/12 by Bangti Jin, Xiliang Lu · 2 citations
Computer Science · Engineering · Mathematics · #Advanced Mathematical Modeling in Engineering #Applied mathematics #Composite Material Mechanics #Conjugate gradient method #Convergence (economics) #Differentiable function #Discretization #Finite element method #Inverse problem #Mathematical analysis #Mathematical optimization #Mathematics #Numerical analysis #Numerical methods in inverse problems #Regularization (linguistics)
paper · pdf · doi:10.1090/s0025-5718-2012-02559-2
openalex publication_date 2012/01/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01
This paper studies a regularization approach for an inverse problem of estimating a spatially-and-temporally dependent Robin coefficient arising in the analysis of convective heat transfer. The parameter-to-state map is analyzed, especially a differentiability result is established. A regularization approach is proposed, and the properties, e.g., existence and optimality system, of the functional are investigated. A finite element method is adopted for discretizing the continuous optimization problem, and the convergence of the finite element approximations as the mesh size and temporal step size tend to zero is established. Numerical results by the conjugate gradient method for one- and two-dimensional problems are presented.