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Licensed Unlicensed Requires Authentication Published by De Gruyter 2022

7 An optimal control problem for equations with p-structure and its finite element discretization

From the book Optimization and Control for Partial Differential Equations

  • Adrian Hirn and Winnifried Wollner


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 W01,p (Ω) to its dual (W01,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.

© 2022 Walter de Gruyter GmbH, Berlin/Boston
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