Robust Multigrid Methods for Discontinuous Galerkin Discretizations of an Elliptic Optimal Control Problem

IF 1 4区数学 Q3 MATHEMATICS, APPLIED

Computational Methods in Applied Mathematics Pub Date : 2024-01-30 DOI:10.1515/cmam-2023-0132

Sijing Liu

引用次数: 0

Abstract

We consider discontinuous Galerkin methods for an elliptic distributed optimal control problem, and we propose multigrid methods to solve the discretized system. We prove that the 𝑊-cycle algorithm is uniformly convergent in the energy norm and is robust with respect to a regularization parameter on convex domains. Numerical results are shown for both 𝑊-cycle and 𝑉-cycle algorithms.

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用于椭圆最优控制问题非连续伽勒金离散化的鲁棒多网格方法

我们考虑了椭圆分布式最优控制问题的非连续 Galerkin 方法，并提出了求解离散系统的多网格方法。我们证明了仸循环算法在能量规范上是均匀收敛的，并且在凸域上与正则化参数有关是稳健的。我们展示了徼循环和 𝑉 循环算法的数值结果。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Computational Methods in Applied Mathematics MATHEMATICS, APPLIED-

CiteScore

2.40

自引率

7.70%

发文量

期刊介绍： The highly selective international mathematical journal Computational Methods in Applied Mathematics　(CMAM) considers original mathematical contributions to computational methods and numerical analysis with applications mainly related to PDEs. CMAM seeks to be interdisciplinary while retaining the common thread of numerical analysis, it is intended to be readily readable and meant for a wide circle of researchers in applied mathematics. The journal is published by De Gruyter on behalf of the Institute of Mathematics of the National Academy of Science of Belarus.