Mark Kärcher

TL;DR: The reduced basis method is employed as a surrogate model for linear-quadratic optimal control problems governed by parametrized elliptic partial dierential equations and it is shown that, based on the as- sumption of parameter dependence, the reduced order optimal control problem and the proposed bounds can be evaluated in an online computational procedure.

TL;DR: The reduced basis method is employed as a surrogate model for the solution of optimal control problems governed by parametrized partial dierential equations (PDEs) and rigorous a posteriori error bounds for the error in the optimal control and the associatederror in the cost functional are developed.

TL;DR: This paper introduces reduced basis spaces not only for the state and adjoint variable but also for the distributed control variable and proposes two different error estimation procedures that provide rigorous bounds for the error in the optimal control and the associated cost functional.

TL;DR: This paper employs the reduced basis method for the efficient and reliable solution of parametrized optimal control problems governed by scalar coercive elliptic partial differential equations and proposes two different reduced basis approximations and associated error estimation procedures.

TL;DR: A certified reduced basis approach for the strong- and weak-constraint four-dimensional variational (4D-Var) data assimilation problem for a parametrized PDE model to generate reduced order approximations for the state, adjoint, initial condition, and model error.