Space-time finite element discretization of parabolic optimal control problems with energy regularization. (English) Zbl 1467.65094
In this study, the authors have analyzed fully unstructured simplicial space-time meshes for the numerical solution of the parabolic optimal control problems with energy regularization in the Bochner space \(L^2(0,T;H^{-1}(\Omega))\). They have established the unique solvability in the continuous case with the help of Babuška’s theorem. Further, they have proved the discrete inf-sup condition for any conforming space-time finite element discretization yielding quasi-optimal discretization error estimates. Finally, they have given several numerical experiments to validate theoretical results.
Reviewer: J. Manimaran (Ponda)
MSC:
| 65M60 | Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs |
| 65M15 | Error bounds for initial value and initial-boundary value problems involving PDEs |
| 65M50 | Mesh generation, refinement, and adaptive methods for the numerical solution of initial value and initial-boundary value problems involving PDEs |
| 35K20 | Initial-boundary value problems for second-order parabolic equations |
| 49J20 | Existence theories for optimal control problems involving partial differential equations |
| 49M41 | PDE constrained optimization (numerical aspects) |
| 49M25 | Discrete approximations in optimal control |
Keywords:
parabolic optimal control problems; space-time finite element methods; discretization error estimatesReferences:
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