论文标题
对Lipschitz多面体的分数半线性最佳控制的错误估计值
Error estimates for fractional semilinear optimal control on Lipschitz polytopes
论文作者
论文摘要
我们采用了分数拉普拉斯操作员的积分定义，并分析了在Lipschitz polictopes上构成的分数，半线性和椭圆形的最佳控制问题的解决方案技术。我们考虑了两种离散化策略：一种半分化的方案，其中可接受的控制集未被离散化，并且是完全离散的方案，其中该集合通过分段常数功能离散化。作为仪器步骤，我们得出了对准均匀和分级网格的分数半椭圆偏微分方程（PDE）的有限元离散估计的误差估计。有了这些估计值，我们会为半分化方案得出误差界限，并改善文献中完全离散方案的误差界限。
We adopt the integral definition of the fractional Laplace operator and analyze solution techniques for fractional, semilinear, and elliptic optimal control problems posed on Lipschitz polytopes. We consider two strategies of discretization: a semidiscrete scheme where the admissible control set is not discretized and a fully discrete scheme where such a set is discretized with piecewise constant functions. As an instrumental step, we derive error estimates for finite element discretizations of fractional semilinear elliptic partial differential equations (PDEs) on quasi-uniform and graded meshes. With these estimates at hand, we derive error bounds for the semidiscrete scheme and improve the ones that are available in the literature for the fully discrete scheme.
