Finite Element Methods for Solving Parabolic Inverse Problems
In this paper, we apply the finite element method to identify physical parameters in parabolic initial-boundary value problems. The identifying problem is formulated as a constrained minimization of the L 2-norm error between the observation data and the physical solution to the original system, with the H 1-regularization or BV-regularization. Then the finite element method is used to approximate the constrained minimization problem, and the resulting discrete system is further reduced to a sequence of unconstrained minimizations. Numerical experiments are presented to show the efficiency of the proposed method, for continuous and discontinuous parameters with noised observations.
KeywordsFinite Element Method Parabolic System Time Step Size Unconstrained Minimization Good Initial Guess
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