Computational algorithms for solving optimal control in linear elasticity. (English) Zbl 07922750
Summary: This paper mainly investigates linear elastic optimal control problems with two constraints: distributed load control and boundary load control. The gradient of the objective functional is derived via an adjoint problem. We obtain the \(\boldsymbol{H^1}\)-regularity for the distributed control solution. Moreover, we establish a suitable finite element interpolation to deal with the non-optimal regularity of the boundary control solution. The error estimates for the fully discretized problems is given. Then, together with the interior point method, a new numerical method for the optimal control of linear elasticity is exhibited. Finally, the effectiveness of presented scheme is demonstrated by various numerical simulations in two and three-space dimensions.
MSC:
| 49M41 | PDE constrained optimization (numerical aspects) |
| 49N10 | Linear-quadratic optimal control problems |
| 74B05 | Classical linear elasticity |
| 65-XX | Numerical analysis |
| 90C51 | Interior-point methods |
Keywords:
linear elasticity; distributed control; boundary control; finite element method; line search methodSoftware:
FreeFem++References:
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