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A new optimal control problem that incorporates the residual of the Eikonal equation into its objective is presented. The formulation of the state equation is based on the level set transport equation but extended by an additional source term, correcting the solution so as to minimize the objective functional. The method enforces the constraint so that the interface cannot be displaced at least in the continuous setting. The system of first-order optimality conditions is derived, linearized, and solved numerically. The control also prevents numerical instabilities, so that no additional stabilization techniques are required. This approach offers the flexibility to include other desired design criteria into the objective functional. The methodology is evaluated numerically in three different examples and compared with other PDE-based reinitialization techniques. Copyright © 2016 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

This paper presents a new approach to reinitialization in finite element methods for the level set transport equation. The proposed variational formulation is derived by solving a minimization problem. A penalty term is introduced to preserve the shape of the free interface in the process of redistancing. In contrast to hyperbolic PDE reinitialization, the resulting boundary value problem is elliptic and can be solved using a simple fixed-point iteration method. The minimization-based approach makes it possible to define the desired geometric properties in terms of a suitable potential function. In particular, truncated distance functions can be generated using a double-well potential. The results of a numerical study indicate that the new methodology is a promising alternative to conventional reinitialization techniques. [ABSTRACT FROM AUTHOR]