Abstract
We study the numerical approximation of elliptic interface optimal control problem by using immersed finite element method in this paper, where the control acts on the interface. The discontinuity of the coefficients across the interface leads to a relatively low regularity of the solution of such problems over the whole domain. In this case, the traditional finite element method cannot solve the state equation and the adjoint state equation well, so we use an immersed finite element method based on uniform mesh to solve the two equations. The control variable is then discretized by a variational discretization method. Finally, a large number of different types of numerical experiments, including complex interfaces, control with constraints, no exact solution, and variable coefficients, validate the effectiveness of this numerical method.
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