Nitsche-XFEM for optimal control problems governed by elliptic PDEs with interfaces
It provides a numerical framework for optimal control with interface conditions, extending existing methods to non-homogeneous interfaces.
The paper presents a Nitsche-XFEM method for optimal control problems governed by elliptic PDEs with interfaces, achieving optimal error estimates in mesh-dependent and L2 norms, validated by numerical experiments.
For the optimal control problem governed by elliptic equations with interfaces, we present a numerical method based on the Hansbo's Nitsche-XFEM. We followed the Hinze's variational discretization concept to discretize the continuous problem on a uniform mesh. We derive optimal error estimates of the state, co-state and control both in mesh dependent norm and L2 norm. In addition, our method is suitable for the model with non-homogeneous interface condition. Numerical results confirmed our theoretical results, with the implementation details discussed.