具有控制约束的椭圆型最优控制问题的双风不连续Galerkin方法的收敛性分析

IF 1.3 Q2 MATHEMATICS, APPLIED

Results in Applied Mathematics Pub Date : 2025-08-01 DOI:10.1016/j.rinam.2025.100624

Satyajith Bommana Boyana , Thomas Lewis , Sijing Liu , Yi Zhang

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引用次数: 0

摘要

研究了一类带控制约束的椭圆型最优控制问题的对称双风不连续Galerkin （DWDG）方法。控制约束是一个椭圆型偏微分方程（PDE），采用对称DWDG方法对其进行离散化。我们推导了状态和伴随状态的能量范数以及控制变量的L2范数中的误差估计。数值实验验证了该方法的鲁棒性和有效性。

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Convergence analysis of a dual-wind discontinuous Galerkin method for an elliptic optimal control problem with control constraints

This paper investigates a symmetric dual-wind discontinuous Galerkin (DWDG) method for solving an elliptic optimal control problem with control constraints. The governing constraint is an elliptic partial differential equation (PDE), which is discretized using the symmetric DWDG approach. We derive error estimates in the energy norm for both the state and the adjoint state, as well as in the