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- W3098082781 abstract "We analyze a reaction coefficient identification problem for the spectral fractional powers of a symmetric, coercive, linear, elliptic, second-order operator in a bounded domain $Omega$. We realize fractional diffusion as the Dirichlet-to-Neumann map for a nonuniformly elliptic problem posed on the semi-infinite cylinder $Omega times (0,infty)$. We thus consider an equivalent coefficient identification problem, where the coefficient to be identified appears explicitly. We derive existence of local solutions, optimality conditions, regularity estimates, and a rapid decay of solutions on the extended domain $(0,infty)$. The latter property suggests a truncation that is suitable for numerical approximation. We thus propose and analyze a fully discrete scheme that discretizes the set of admissible coefficients with piecewise constant functions. The discretization of the state equation relies on the tensorization of a first-degree FEM in $Omega$ with a suitable $hp$-FEM in the extended dimension. We derive convergence results and obtain, under the assumption that in neighborhood of a local solution the second derivative of the reduced cost functional is coercive, a priori error estimates." @default.
- W3098082781 created "2020-11-23" @default.
- W3098082781 creator A5009899286 @default.
- W3098082781 creator A5044773525 @default.
- W3098082781 date "2019-03-22" @default.
- W3098082781 modified "2023-09-27" @default.
- W3098082781 title "A reaction coefficient identification problem for fractional diffusion" @default.
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- W3098082781 doi "https://doi.org/10.1088/1361-6420/ab0127" @default.
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