多尺度系数的椭圆最优控制问题的多重调和样条方法
Rough Polyharmonic Splines Method forOptimal Control Problem Governed by Elliptic Systems with Rough Coefficient
摘要: 多重调和样条方法(RPS)是为解决具有多尺度系数问题的一种变分方法。RPS方法不依赖于遍历性或尺度分离的概念，而是依赖于解空间的紧致性。本文将RPS方法应用到具有多尺度系数的椭圆型最优控制问题，空间离散采用RPS基底,得到多尺度最优控制问题的误差估计。
Abstract: Rough polyharmonic splines (RPS) is a variational method which has recently been developed for linear divergence-form operators with arbitrary rough coefficients. RPS method does not rely on concepts of ergodicity or scale-separation, but on compactness properties of the solution space. This paper is applies the RPS method to elliptic optimal control problems with multi-scale coefficients, using the RPS basis for spatial discretization to obtain the error estimates of the multi-scale optimal control problem.
文章引用：曾焦燕. 多尺度系数的椭圆最优控制问题的多重调和样条方法[J]. 理论数学, 2024, 14(12): 56-64. https://doi.org/10.12677/PM.2024.1412406

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