Adaptive mixed finite element methods for nonlinear optimal control problems

In this paper we study the mixed finite element discretization for general optimal control problems governed by nonlinear elliptic equations. We derive a posteriori error estimates for the coupled state and control approximation. Such a posteriori error estimates can be used to construct more efficient and reliable adaptive mixed finite element method for optimal control problems. Next we introduce an adaptive algorithm to guide the mesh refinement. Finally, we present a numerical example which confirm our theoretical results.

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