1. Lq-regularization for the inverse Robin problem.
- Author
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Fan, Qibin, Jiao, Yuling, Lu, Xiliang, and Sun, Zhiyuan
- Subjects
MATHEMATICAL regularization ,LEAST squares ,COMPUTER simulation ,FINITE element method ,DISCRETIZATION methods - Abstract
In this paper, an inverse Robin problem for an elliptic equation is investigated. The Robin coefficient is assumed to be a small perturbation from a reference coefficient, hence a sparse structure is a priori known. An L
q -regularized output least square formulation is considered with q ∈ (0,1). The existence of the minimizer is proved. The convergence of the finite element discretization with respect to mesh size is shown. A modified Newton algorithm is applied to solve the smoothing first order optimality system. Two-dimensional and three-dimensional numerical examples demonstrate the efficiency of the proposed method. [ABSTRACT FROM AUTHOR]- Published
- 2016
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