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A Frame Work for the Error Analysis of Discontinuous Finite Element Methods for Elliptic Optimal Control Problems and Applications to IP methods
In this article, an abstract framework for the error analysis of
discontinuous Galerkin methods for control constrained optimal control problems
is developed. The analysis establishes the best approximation result from a
priori analysis point of view and delivers reliable and efficient a posteriori
error estimators. The results are applicable to a variety of problems just
under the minimal regularity possessed by the well-posed ness of the problem.
Subsequently, applications of interior penalty methods for a boundary
control problem as well as a distributed control problem governed by the
biharmonic equation subject to simply supported boundary conditions are
discussed through the abstract analysis. Numerical experiments illustrate the
theoretical findings. Finally, we also discuss the variational discontinuous
discretization method (without discretizing the control) and its corresponding
error estimates.Comment: 23 pages, 5 figures, 1 tabl
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