A posteriori error estimates for mixed finite element approximation of nonlinear quadratic optimal control problems

摘要

In this paper, we obtain an a posteriori error analysis for mixed finite element approximation of convex optimal control problems governed by a nonlinear second-order elliptic equation. Our results are based on the approximation for both the coupled state variables and the control variable. We propose to improve the error estimates, which can be used to construct an adaptive finite element scheme. A numerical example demonstrating our theoretical results is also presented in this paper.