Error estimates for the numerical approximation of a distributed optimal control problem governed by the von Kármán equations
Provides theoretical error bounds for numerical solutions of a specific nonlinear optimal control problem in structural mechanics.
The paper derives a priori error estimates for finite element discretization of an optimal control problem governed by von Kármán equations in polygonal domains with control constraints, and validates them numerically.
In this paper, we discuss the numerical approximation of a distributed optimal control problem governed by the von Karman equations, defined in polygonal domains with point-wise control constraints. Conforming finite elements are employed to discretize the state and adjoint variables. The control is discretized using piece-wise constant approximations. A priori error estimates are derived for the state, adjoint and control variables under minimal regularity assumptions on the exact solution. Numerical results that justify the theoretical results are presented.