A posteriori error control of a state constrained elliptic control problem. (English) Zbl 1161.65049
The authors study the a posteriori error control of a state constrained elliptic control problem. First they give the mathematical setting of the problem, then they sketch the finite element discretization of the problem and derive the corresponding optimality system and state some properties of the discrete approximations to \(y, p, u\) and to the Lagrange multipliers \(\mu^{a}, \mu^{b}\) corresponding to the lower and upper state constraint. Later they specify the local error indicators and test their effectivity by means of numerical examples.
Reviewer: Seenith Sivasundaram (Daytona Beach)
MSC:
| 65K10 | Numerical optimization and variational techniques |
| 49J20 | Existence theories for optimal control problems involving partial differential equations |
| 49M25 | Discrete approximations in optimal control |
Keywords:
elliptic optimal control problem; state constraints; goal-oriented adaptivity; a posteriori error control; finite element; numerical examplesReferences:
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