Name
Title | ||
|---|---|---|
Optimization with Respect to Order in a Fractional Diffusion Model: Analysis, Approximation and Algorithmic Aspects. |
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. |
Year | DOI | Venue |
|---|---|---|
2018 | 10.1007/s10915-018-0703-0 | J. Sci. Comput. |
Keywords | Field | DocType |
Optimal control problems, Identification (inverse) problems, Fractional diffusion, Bisection algorithm, Finite elements, Stability, Fully-discrete methods, Convergence, 26A33, 35J70, 49J20, 49K21, 49M25, 65M12, 65M15, 65M60 | Convergence (routing),Inverse,Uniqueness,Mathematical optimization,Bisection method,Mathematical analysis,Finite element method,Operator (computer programming),Elliptic curve,Mathematics,Parameter identification problem | Journal |
Volume | Issue | ISSN |
77 | 1 | 0885-7474 |
Citations | PageRank | References |
2 | 0.38 | 3 |
Authors | ||
3 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| H. Antil | 1 | 71 | 10.56 |
| Enrique Otárola | 2 | 86 | 13.91 |
| Abner J. Salgado | 3 | 105 | 13.27 |