Abstract
In this paper, we investigate a characteristic finite element approximation of quadratic optimal control problems governed by linear advection-dominated diffusion equations, where the state and co-state variables are discretized by piecewise linear continuous functions and the control variable is approximated by piecewise constant functions. We derive some a priori error estimates for both the control and state approximations. It is proved that these approximations have convergence order \(\mathcal{O}(h_{U}+h+k)\) , where h U and h are the spatial mesh-sizes for the control and state discretization, respectively, and k is the time increment. Numerical experiments are presented, which verify the theoretical results.
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This research was supported by the National Basic Research Program of China (No. 2007CB814906) and the National Natural Science Foundation of China (No. 10771124).
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Fu, H., Rui, H. A Priori Error Estimates for Optimal Control Problems Governed by Transient Advection-Diffusion Equations. J Sci Comput 38, 290–315 (2009). https://doi.org/10.1007/s10915-008-9224-6
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DOI: https://doi.org/10.1007/s10915-008-9224-6