论文标题
部分可观测时空混沌系统的无模型预测
Robust finite element discretization and solvers for distributed elliptic optimal control problems
论文作者
论文摘要
我们考虑标准跟踪类型，分布式椭圆形的最佳控制问题，$ l^2 $正则化及其有限的元素离散化。我们正在调查有限元近似值$ u _ {\ varrho h} $之间的$ l^2 $错误事实证明，对于正规化参数的这种选择，我们可以设计简单的类似Jacobi的预处理的微小矿石或Bramble-Pasciak CG方法，使我们能够在相对于算术操作和内存需求方面求解降低的离散最佳系统中的离散最佳系统。理论上的结果通过几个基准问题与各种规律性（包括不连续目标）的目标进行了证实。
We consider standard tracking-type, distributed elliptic optimal control problems with $L^2$ regularization, and their finite element discretization. We are investigating the $L^2$ error between the finite element approximation $u_{\varrho h}$ of the state $u_\varrho$ and the desired state (target) $\bar{u}$ in terms of the regularization parameter $\varrho$ and the mesh size $h$ that leads to the optimal choice $\varrho = h^4$. It turns out that, for this choice of the regularization parameter, we can devise simple Jacobi-like preconditioned MINRES or Bramble-Pasciak CG methods that allow us to solve the reduced discrete optimality system in asymptotically optimal complexity with respect to the arithmetical operations and memory demand. The theoretical results are confirmed by several benchmark problems with targets of various regularities including discontinuous targets.
