C0 interior penalty methods for an elliptic distributed optimal control problem
Abstract: We consider C0 interior penalty methods for a
linear-quadratic elliptic distributed optimal control problem with
pointwise state constraints in two spatial dimensions, where the cost
function tracks the state at points, curves and regions of the
domain. Here we reformulate the optimal control problem into a problem
that only involves the state, which is equivalent to a fourth-order
variational inequality. We derive the Karush-Kuhn-Tucker conditions
from the variational inequality and find the regularity result of the
solution. The reduced minimization problem is solved by a C0 interior
penalty method. The discrete problem is solved efficiently by the
primal-dual active set algorithm. We provide a convergence analysis
and demonstrate the performance of the method through several
numerical experiments.
Last modified: Tue Apr 2 11:08:24 EDT 2024