Jin, B;
Li, B;
Zhou, Z;
(2018)
Pointwise-in-time error estimates for an optimal control problem with subdiffusion constraint.
IMA Journal of Numerical Analysis
, 40
(1)
pp. 377-404.
10.1093/imanum/dry064.
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Abstract
In this work, we present numerical analysis for a distributed optimal control problem, with box constraint on the control, governed by a subdiffusion equation which involves a fractional derivative of order α ∈ (0;1) in time. The fully discrete scheme is obtained by applying the conforming linear Galerkin finite element method in space, L1 scheme/backward Euler convolution quadrature in time, and the control variable by a variational type discretization. With a space mesh size h and time stepsize t, we establish the following order of convergence for the numerical solutions of the optimal control problem O(t^{(min(1/2+α-ε, 1)} +h²) in the discrete L²(0;T;L²(Ω)) norm and O(t^{α-ε} + l^{2/h}h²) in the discrete L∞(0;T;L²(Ω)) norm, with any small ε > 0 and l_{h} = ln(2+1/h). The analysis relies essentially on the maximal Lp-regularity and its discrete analogue for the subdiffusion problem. Numerical experiments are provided to support the theoretical results.
| Type: | Article |
|---|---|
| Title: | Pointwise-in-time error estimates for an optimal control problem with subdiffusion constraint |
| Open access status: | An open access version is available from UCL Discovery |
| DOI: | 10.1093/imanum/dry064 |
| Publisher version: | https://doi.org/10.1093/imanum/dry064 |
| Language: | English |
| Additional information: | This version is the author accepted manuscript. For information on re-use, please refer to the publisher’s terms and conditions. |
| Keywords: | optimal control, time-fractional diffusion, L1 scheme, convolution quadrature, pointwise-in-time error estimate, maximal regularity |
| UCL classification: | UCL UCL > Provost and Vice Provost Offices > UCL BEAMS UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Engineering Science UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Engineering Science > Dept of Computer Science |
| URI: | https://discovery.ucl.ac.uk/id/eprint/10056720 |
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