论文标题
抛物线分布式最佳控制问题的时空有限元方法
Space-time finite element methods for parabolic distributed optimal control problems
论文作者
论文摘要
我们提出了一种通过抛物线偏微分方程约束的分布式最佳控制问题的数值近似的方法。我们通过最近开发的抛物线方程的时空变异公式来补充一阶最佳条件，该方程在能量规范中是强制性的，也是Lagrangian乘数。我们的最终配方符合持续和离散水平的Babuška-Brezzi条件，而无需限制。因此，我们可以允许最终的期望状态，并获得有效且可靠的A-tosteriori误差估计器。数值实验证实了我们的理论发现。
We present a method for the numerical approximation of distributed optimal control problems constrained by parabolic partial differential equations. We complement the first-order optimality condition by a recently developed space-time variational formulation of parabolic equations which is coercive in the energy norm, and a Lagrangian multiplier. Our final formulation fulfills the Babuška-Brezzi conditions on the continuous as well as discrete level, without restrictions. Consequently, we can allow for final-time desired states, and obtain an a-posteriori error estimator which is efficient and reliable. Numerical experiments confirm our theoretical findings.
