Efficient numerical solution of parabolic optimization problems by finite element methods. (English) Zbl 1135.35317
In the present study the authors discuss efficient numerical methods for solving optimization problems governed by parabolic partial differential equations. The optimization problems are formulated in a general setting including optimal control as well as parameter identification problems. Both, time and space discretization are based on the finite element method. The authors suggest an algorithm, which allows to reduce the required storage. They analyze the complexity of this algorithm and prove that the required storage grows only logarithmic with respect to the number of time intervals.
Reviewer: Messoud A. Efendiev (Berlin)
MSC:
| 35B37 | PDE in connection with control problems (MSC2000) |
| 35K55 | Nonlinear parabolic equations |
| 35K90 | Abstract parabolic equations |
| 49K20 | Optimality conditions for problems involving partial differential equations |
| 49M05 | Numerical methods based on necessary conditions |
| 49M29 | Numerical methods involving duality |
| 65N30 | Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs |
Software:
revolveReferences:
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