Chapter 19: Inverse problems with additional model uncertainty
Abstract
In an inverse problem governed by a system of PDEs, we typically seek to estimate an inversion parameter while assuming full knowledge of the remaining model parameters. Let us consider an example. Recall the inverse problem from Exercise 9.5, where the goal was to estimate the boundary term \(m\) in\[-\nabla\cdot (\kappa\nabla u)=f\quad \text{in}\ \mathcal{D},\](19.1)\[u = S_D \quad \text{on}\ \Gamma_{\text D},\](19.2)\[\kappa\nabla u\cdot \boldsymbol n = S_N \quad \text{on}\ \Gamma_{\text N},\](19.3)\[\kappa\nabla u\cdot \boldsymbol n + e^m u = S_R \quad \text{on}\ \Gamma_{\text R}.\](19.4)
Fields of Study & Subjects
Numerical methods in inverse problems
Advanced Numerical Methods in Computational Mathematics
Differential Equations and Boundary Problems
Publication details
- Journal / source
- Society for Industrial and Applied Mathematics eBooks
- Pages
- 263–268
- Publication date
- 27 February 2026
- Language
- EN
- Document type
- Book chapter