Abstract
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.
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Keung, Y.L., Zou, J. (2000). Finite Element Methods for Solving Parabolic Inverse Problems. In: Frenk, H., Roos, K., Terlaky, T., Zhang, S. (eds) High Performance Optimization. Applied Optimization, vol 33. Springer, Boston, MA. https://doi.org/10.1007/978-1-4757-3216-0_15
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DOI: https://doi.org/10.1007/978-1-4757-3216-0_15
Publisher Name: Springer, Boston, MA
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