An anisotropic mesh adaptation procedure for an optimal control problem of the advection-diffusion-reaction equation

Code:
15/2008
Title:
An anisotropic mesh adaptation procedure for an optimal control problem of the advection-diffusion-reaction equation
Date:
Wednesday 2nd July 2008
Author(s):
Micheletti, Stefano; Perotto, Simona
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Abstract:
We derive an anisotropic a posteriori error estimator for a PDE-con- strained optimal control problem, governed by the scalar advection-diffusion- reaction equation. With a view to the advection dominated case, a strongly consistent symmetric stabilization is employed so that the “optimize-then- discretize” and “discretize-then-optimize” philosophies coincide and lead to the same discrete problem. The estimator is turned into an anisotropic mesh adaptation procedure which allows us to approximate the cost func- tional within to a given tolerance. Both an academic and a realistic test, inspired by an environmental application, assess the performance of the proposed approach.