Adaptive Finite Element Approximation for an Elliptic Optimal Control Problem with Both Pointwise and Integral Control Constraints

作者：Du, Ning; Ge, Liang; Liu, Wenbin^*

来源：Journal of Scientific Computing, 2014, 60(1): 160-183.

DOI：10.1007/s10915-013-9790-0

• Optimal control problem
• Finite element approximation
• Adaptive finite element method
• A posteriori error estimates
• Multi-meshes

In this paper, we study the adaptive finite element approximation for a constrained optimal control problem with both pointwise and integral control constraints. We first obtain the explicit solutions for the variational inequalities both in the continuous and discrete cases. Then a priori error estimates are established, and furthermore equivalent a posteriori error estimators are derived for both the state and the control approximation, which can be used to guide the mesh refinement for an adaptive multi-mesh finite element scheme. The a posteriori error estimators are implemented and tested with promising numerical results.

• 出版日期2014-7
• 单位山东大学