A posteriori error estimation for finite element approximations of a PDE-constrained optimization problem in fluid dynamics
Abstract
We derive globally reliable a posteriori error estimators for a PDE-constrained optimization problem involving linear models in fluid dynamics as state equation; control constraints are also considered. The corresponding local error indicators are locally efficient. The assumptions under which we perform the analysis are such that they can be satisfied for a wide variety of stabilized finite element methods as well as for standard finite element methods. When stabilized methods are considered, no a priori relation between the stabilization terms for the state and adjoint equations is required. If a lower bound for the inf-sup constant is available, a posteriori error estimators that are fully computable and provide guaranteed upper bounds on the norm of the error can be obtained. We illustrate the theory with numerical examples.
Cite
@article{arxiv.1708.00590,
title = {A posteriori error estimation for finite element approximations of a PDE-constrained optimization problem in fluid dynamics},
author = {Alejandro Allendes and Enrique Otarola and Richard Rankin},
journal= {arXiv preprint arXiv:1708.00590},
year = {2017}
}