The purpose of this work is the development of space-time discretization schemes for phase-field optimal control problems. First, a time discretization of the forward problem is derived using a discontinuous Galerkin formulation. Here, a challenge is to include regularization terms and the crack irreversibility constraint. The optimal control setting is formulated by means of the Lagrangian approach from which the primal part, adjoint, tangent and adjoint Hessian are derived. Herein the overall Newton algorithm is based on a reduced approach by eliminating the state constraint. From the low-order discontinuous Galerkin discretization, adjoint time-stepping schemes are finally obtained.

翻译：这项工作的目的是为阶段-实地最佳控制问题制定时间分解计划。首先,用不连续的Galerkin配方得出远期问题的时间分解,这里的一个挑战是包括正规化条款和快速不可逆转限制。最佳控制设置是通过拉格朗加办法制定的,从中得出原始部分、联合、正切和联合的赫森。这里,总体牛顿算法的基础是通过消除国家限制而减少方法。从低顺序的连续加勒金分解中,最终获得了联合时间跨入计划。