论文标题
由非线性双曲线保护法律控制的最佳控制问题中的三阶加权基本上是非振荡方案
A Third-Order Weighted Essentially Non-Oscillatory Scheme in Optimal Control Problems Governed by Nonlinear Hyperbolic Conservation Laws
论文作者
论文摘要
加权本质上是非振荡（WENO）方法是非线性双曲线偏微分方程的流行和有效的空间离散方法。尽管存在冲击时，这些方法是正式的一阶准确度，但直到电击位置，它们仍然具有均匀的高阶精度。在本文中，我们提出了一种新型的三阶数值方法，用于解决符合标量非线性双曲线保护定律的最佳控制问题。它基于第一分化 - 最优化的方法，并将三阶的离散伴随WENO方案与经典的强稳定性保留了三阶段的三阶runge-kutta方法SSPRK3。我们分析其近似属性，并将其应用于具有非平滑目标状态的跟踪类型的最佳控制问题。与常见的一阶方法（如宽松液化和渗透方法）的比较表明，它具有更高准确性的巨大潜力，以及围绕不连续性的良好分辨率。
The weighted essentially non-oscillatory (WENO) methods are popular and effective spatial discretization methods for nonlinear hyperbolic partial differential equations. Although these methods are formally first-order accurate when a shock is present, they still have uniform high-order accuracy right up to the shock location. In this paper, we propose a novel third-order numerical method for solving optimal control problems subject to scalar nonlinear hyperbolic conservation laws. It is based on the first-disretize-then-optimize approach and combines a discrete adjoint WENO scheme of third order with the classical strong stability preserving three-stage third-order Runge-Kutta method SSPRK3. We analyze its approximation properties and apply it to optimal control problems of tracking-type with non-smooth target states. Comparisons to common first-order methods such as the Lax-Friedrichs and Engquist-Osher method show its great potential to achieve a higher accuracy along with good resolution around discontinuities.
