ACCURACY AND CONVERGENCE PROPERTIES OF THE FINITE DIFFERENCE MULTIGRID SOLUTION OF AN OPTIMAL CONTROL OPTIMALITY SYSTEM
The finite difference multigrid solution of an optimal control problem associated with
an elliptic equation is considered. Stability of the finite difference optimality system and optimalorder
error estimates in the discrete L2 normand in the discrete H1 normunder minimumsm oothness
requirements on the exact solution are proved. Sharp convergence factor estimates of the two grid
method for the optimality system are obtained by means of local Fourier analysis. A multigrid
convergence theory is provided which guarantees convergence of the multigrid process towards weak
solutions of the optimality system.
- Issue Date
- 2003
- Keywords
optimal control problem; Poisson equation; finite differences; accuracy estimate; convergence theory; multigrid method
- Citation
SIAM J. on Control and Optimization, Vol.41, No.5, pp.1477-1497
- ISSN
- 0363-0129; 1095-7138
- Appears in Collection
- MA-Journal Papers(저널논문)
- Files in This Item
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