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An adaptive moving mesh method for optimal control problems in viscous incompressible fluid is proposed with the incompressible Navier–Stokes system used to describe the motion of the fluid. The moving distance of nodes in the adopted mesh moving strategy is found by solving a diffusion equation with source terms, and an algorithm that fully considers the characteristics of the control problem is given with symmetry reduction to the incompressible Navier–Stokes equations. Numerical examples are provided to show that the proposed algorithm can solve the optimal control problem stably and efficiently on the premise of ensuring high precision.

An Adaptive Moving Mesh Method for Solving Optimal Control Problems in Viscous Incompressible Fluid