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

• 作者: Quanxiang Wang
• 来源期刊: 应用数学(英文)
• 学科: 数学
• 关键词: Finite Volume Element Neumann Boundary Control Variational Discretization
• 年，卷（期）: 2020,（12）
• 页码范围: 1243-1252
• 页数: 10页
• 分类号: O17

摘要

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 <em>L</em>² (Γ) and <em>L</em>^∞ (Γ) norm. For state and adjoint state, optimal convergence order in the <em>L</em>² (Ω) and <em>H</em>¹ (Ω) can also be obtained.