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Journal of Scientific Computing

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28-03-2018

Optimization with Respect to Order in a Fractional Diffusion Model: Analysis, Approximation and Algorithmic Aspects

Authors: Harbir Antil, Enrique Otárola, Abner J. Salgado

Published in: Journal of Scientific Computing | Issue 1/2018

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Abstract

We consider an identification (inverse) problem, where the state \({\mathsf {u}}\) is governed by a fractional elliptic equation and the unknown variable corresponds to the order \(s \in (0,1)\) of the underlying operator. We study the existence of an optimal pair \(({\bar{s}}, {{\bar{{\mathsf {u}}}}})\) and provide sufficient conditions for its local uniqueness. We develop semi-discrete and fully discrete algorithms to approximate the solutions to our identification problem and provide a convergence analysis. We present numerical illustrations that confirm and extend our theory.

previous article Correction to: The BR1 Scheme is Stable for the Compressible Navier–Stokes Equations

next article Stability and Convergence Analysis of a Class of Continuous Piecewise Polynomial Approximations for Time-Fractional Differential Equations

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Title: Optimization with Respect to Order in a Fractional Diffusion Model: Analysis, Approximation and Algorithmic Aspects
Authors: Harbir Antil
Enrique Otárola
Abner J. Salgado
Publication date: 28-03-2018
Publisher: Springer US
Published in: Journal of Scientific Computing / Issue 1/2018
Print ISSN: 0885-7474
Electronic ISSN: 1573-7691
DOI: https://doi.org/10.1007/s10915-018-0703-0

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