Error estimates of characteristic finite elements for bilinear convection-diffusion optimal control problems. (English) Zbl 07878048
Summary: This paper investigates a fully discrete characteristic finite element approximation of bilinear unsteady convection-diffusion optimal control problems. The characteristic line method is used to treat the convection term and the finite element method is adopted to treat the diffusion term. The state and adjoint state are discretized by piecewise linear functions, the control is approximated by piecewise constant functions. A priori error estimates are derived for the state, adjoint state and control variables. Some numerical examples are provided to confirm our theoretical findings.
MSC:
| 49M25 | Discrete approximations in optimal control |
| 65M60 | Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs |
Keywords:
characteristic finite elements; error estimates; bilinear convection-diffusion optimal control problemsSoftware:
AFEPackReferences:
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