Back to Search
Start Over
Heterogeneous multiscale method for optimal control problem governed by parabolic equation with highly oscillatory coefficients
- Source :
- Journal of Computational and Applied Mathematics. 328:116-131
- Publication Year :
- 2018
- Publisher :
- Elsevier BV, 2018.
-
Abstract
- In this paper, we investigate the heterogeneous multiscale method (HMM) for the optimal control problem governed by the parabolic equation with highly oscillatory coefficients. The state variable and adjoint state variable are approximated by the multiscale discretization scheme that relies on coupled macro and micro finite elements, while the control variable is discretized by the piecewise constants. By applying the well-known Lions’ Lemma to the discretized optimal control problem, we obtain the necessary and sufficient optimality conditions. A priori error estimates are derived for the state, co-state and the control with uniform bounded constants. Finally, numerical results are presented to illustrate our theoretical findings.
- Subjects :
- State variable
Discretization
Applied Mathematics
Mathematical analysis
MathematicsofComputing_NUMERICALANALYSIS
Control variable
010103 numerical & computational mathematics
Optimal control
01 natural sciences
Finite element method
010101 applied mathematics
Computational Mathematics
Bounded function
Piecewise
A priori and a posteriori
0101 mathematics
Mathematics
Subjects
Details
- ISSN :
- 03770427
- Volume :
- 328
- Database :
- OpenAIRE
- Journal :
- Journal of Computational and Applied Mathematics
- Accession number :
- edsair.doi...........7e18e6f3f1cd764aafba60340826b20c