A Priori Error Estimates for Optimal Control Problems Governed by Transient Advection-Diffusion Equations

作者：Fu Hongfei; Rui Hongxing^*

来源：Journal of Scientific Computing, 2009, 38(3): 290-315.

DOI：10.1007/s10915-008-9224-6

• Characteristic finite element
• Optimal control problems
• Advection-dominated diffusion equations
• A priori error estimates

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 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.

• 出版日期2009-3
• 单位山东大学