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Adaptive finite element methods for optimal control of partial differential equations: Basic concept. (English) Zbl 0967.65080

For the optimal control problem of a system described by elliptic partial differential equations and solved using discretization a new approach of error control and mesh adaptivity is proposed. The Lagrangian formalism yields the first-order necessary optimality condition in the form of an indefinite boundary value problem which is approximated by an adaptive Galerkin finite element method. The mesh design in the resulting reduced models is controlled by residual-based a posteriori error estimates.
The result of the investigation given in the paper is a generic simple algorithm for mesh adaptation within the optimization process. A test example of the method for simple boundary control problems in semiconductor models is given.

MSC:

65K10 Numerical optimization and variational techniques
49M15 Newton-type methods
82D37 Statistical mechanics of semiconductors
49K20 Optimality conditions for problems involving partial differential equations
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