A coupled complex boundary method for parameter identification in elliptic problems
- 7 April 2019
- journal article
- research article
- Published by Taylor & Francis Ltd in International Journal of Computer Mathematics
- Vol. 97 (5), 998-1015
- https://doi.org/10.1080/00207160.2019.1601181
Abstract
In this paper, we study a parameter identification problem for elliptic partial differential equations. We reconstruct the coefficient with additional boundary measurements, including both Dirichlet and Neumann boundary conditions. To solve the problem, the coupled complex boundary method(CCBM), originally proposed in [12] is used. With CCBM, a complex boundary problem is introduced in such a way that the boundary conditions are coupled in a complex Robin boundary condition with a parameter τ. Using Tikhonov regularization, the coefficient is sought such that the imaginary part of the solution of the forward Robin boundary value problem vanishes in the problem domain, which brings advantages on robustness in reconstruction. Besides, the reconstruction is feasible even for very small regularization parameter through choosing the values of τ properly. Some theoretical analyses are given. Moreover, noise model is analyzed and the finite element method is used for discretization. Numerical examples show the feasibility and stability of the proposed method.Keywords
Funding Information
- Natural Science Foundation of Hunan Province (2016JJ4122)
- National Natural Science Foundation of China (11526194)
This publication has 19 references indexed in Scilit:
- Numerical estimation of the Robin coefficient in a stationary diffusion equationIMA Journal of Numerical Analysis, 2009
- A new general mathematical framework for bioluminescence tomographyComputer Methods in Applied Mechanics and Engineering, 2008
- The output least-squares approach to estimating Lamé moduliInverse Problems, 2007
- Iterative regularization for elliptic inverse problemsComputers & Mathematics with Applications, 2007
- Bioluminescence tomography with optimized optical parametersInverse Problems, 2007
- A piecewise constant level set method for elliptic inverse problemsApplied Numerical Mathematics, 2007
- Mathematical theory and numerical analysis of bioluminescence tomographyInverse Problems, 2006
- Identification of Discontinuous Coefficients in Elliptic Problems Using Total Variation RegularizationSIAM Journal on Scientific Computing, 2003
- Convergence of Tikhonov regularization for constrained ill-posed inverse problemsInverse Problems, 1994
- Convergence rates for Tikhonov regularisation of non-linear ill-posed problemsInverse Problems, 1989