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• W2951889563 abstract "The problem of identifying the diffusion parameter appearing in a nonlocal steady diffusion equation is considered. The identification problem is formulated as an optimal control problem having a matching functional as the objective of the control and the parameter function as the control variable. The analysis makes use of a nonlocal vector calculus that allows one to define a variational formulation of the nonlocal problem. In a manner analogous to the local partial differential equations counterpart, we demonstrate, for certain kernel functions, the existence of at least one optimal solution in the space of admissible parameters. We introduce a Galerkin finite element discretization of the optimal control problem and derive a priori error estimates for the approximate state and control variables. Using one-dimensional numerical experiments, we illustrate the theoretical results and show that by using nonlocal models it is possible to estimate non-smooth and discontinuous diffusion parameters." @default.
• W2951889563 created "2019-06-27" @default.
• W2951889563 creator A5028709260 @default.
• W2951889563 creator A5076283476 @default.
• W2951889563 date "2013-10-09" @default.
• W2951889563 modified "2023-09-27" @default.
• W2951889563 title "Identification of the diffusion parameter in nonlocal steady diffusion problems" @default.
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• W2951889563 hasPublicationYear "2013" @default.
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