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For the optimal control problem governed by elliptic equations withinterfaces, we present a numerical method based on the Hansbo's Nitsche-XFEM.We followed the Hinze's variational discretization concept to discretize thecontinuous problem on a uniform mesh. We derive optimal error estimates of thestate, co-state and control both in mesh dependent norm and L2 norm. Inaddition, our method is suitable for the model with non-homogeneous interfacecondition. Numerical results confirmed our theoretical results, with theimplementation details discussed.

Nitsche-XFEM for optimal control problems governed by elliptic PDEs with interfaces