Finite Volume Element Method for Solving the Elliptic Neumann Boundary Control Problems

IF 1 4区数学

Applied Mathematics-A Journal of Chinese Universities Series B Pub Date : 2020-12-08 DOI:10.4236/am.2020.1112085

Quanxiang Wang

引用次数: 0

Abstract

Solving optimization problems with partial differential equations constraints is one of the most challenging problems in the context of industrial applications. In this paper, we study the finite volume element method for solving the elliptic Neumann boundary control problems. The variational discretization approach is used to deal with the control. Numerical results demonstrate that the proposed method for control is second-order accuracy in the L2 (Γ) and L∞ (Γ) norm. For state and adjoint state, optimal convergence order in the L2 (Ω) and H1 (Ω) can also be obtained.

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求解椭圆型Neumann边界控制问题的有限体积元法

求解带有偏微分方程约束的优化问题是工业应用中最具挑战性的问题之一。本文研究了求解椭圆型Neumann边界控制问题的有限体积元方法。采用变分离散化方法进行控制。数值结果表明，所提出的控制方法在L2范数(Γ)和L∞范数(Γ)上具有二阶精度。对于状态和伴随状态，也可以得到L2 (Ω)和H1 (Ω)的最优收敛阶。

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

Applied Mathematics-A Journal of Chinese Universities Series B MATHEMATICS, APPLIED-

自引率

10.00%

发文量

期刊介绍： Applied Mathematics promotes the integration of mathematics with other scientific disciplines, expanding its fields of study and promoting the development of relevant interdisciplinary subjects. The journal mainly publishes original research papers that apply mathematical concepts, theories and methods to other subjects such as physics, chemistry, biology, information science, energy, environmental science, economics, and finance. In addition, it also reports the latest developments and trends in which mathematics interacts with other disciplines. Readers include professors and students, professionals in applied mathematics, and engineers at research institutes and in industry. Applied Mathematics - A Journal of Chinese Universities has been an English-language quarterly since 1993. The English edition, abbreviated as Series B, has different contents than this Chinese edition, Series A.