7 An optimal control problem for equations with p-structure and its finite element discretization
Adrian Hirn, Winnifried Wollner · 2022
We analyze a finite element approximation of an optimal control problem that involves an elliptic equation with p-structure (e. g., the p-Laplace) as a constraint. As the nonlinear operator related to the p-Laplace equation mapping the space W 0 1,p (Ω) to its dual (W 0 1,p (Ω))* is not Gâteaux differentiable, first-order optimality conditions cannot be formulated in a standard way. Without using adjoint information, we derive novel a priori error estimates for the convergence of the cost functional for both variational discretization and piecewise constant controls.