Numerical approximation and analysis of the inverse Robin problem using the Kohn-Vogelius method
Year: 2026
Type: article
Abstract: In this work, we numerically investigate the inverse Robin problem of recovering a piecewise constant Robin coefficient in an elliptic or parabolic problem from the Cauchy data on a part of the boundary, which arises commonly in several applications, e.g., non-destructive corrosion detection. We employ a Kohn-Vogelius type variational functional for the regularized reconstruction, and discretize the resulting optimization problem using the Galerkin finite element method on a graded mesh. We establish rigorous error estimates on the recovered Robin coefficient in terms of the mesh size, temporal step size and noise level. This is achieved by combining the approximation error of the direct problem, a priori estimates on the functional, and suitable conditional stability estimates of the continuous inverse problem. We present several numerical experiments to illustrate the approach and to complement the theoretical findings.
Source: Mathematics of Computation
DOI: 10.1090/mcom/4222
Authors: Erik Burman, Siyu Cen, Bangti Jin, Zhi Zhou
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: hybrid
Awards: G1282174418, Quantitative estimates of discretisation and modelling errors in variational data assimilation for incompressible flows, G4210022139, Computational methods for inverse problems subject to wave equations in heterogeneous media, G4596482654, G5931411422, G5970602439, G6438284693, G8134434530, G8533909178
OpenAlex ID: W4417129302
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