Stabilization and adaptive FEM for optimal control problems of stationary convection-dominated diffusion equations on surfaces

IF 2.4 2区数学 Q1 MATHEMATICS, APPLIED

Applied Numerical Mathematics Pub Date : 2025-04-29 DOI:10.1016/j.apnum.2025.04.009

Qiuhui Yan, Xufeng Xiao, Xinlong Feng

引用次数: 0

Abstract

This paper explores the optimal control problem for the stationary convection-dominated diffusion equation on surfaces, employing stabilization and adaptive finite element methods as numerical approaches. We propose an optimal system on surfaces, demonstrate the existence and uniqueness of the solution, and analyze the relevant finite element theory. To mitigate oscillation phenomena, we adopt the streamline diffusion stabilization method. To enhance computational efficiency and achieve high-resolution numerical solutions with fewer degrees of freedom, we integrate the streamline diffusion method with adaptive mesh refinement. Finally, numerical experiments confirm the advantages of our approach.

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表面上以对流为主的平稳扩散方程最优控制问题的镇定与自适应有限元分析

本文采用稳定法和自适应有限元法研究了表面上以对流为主的平稳扩散方程的最优控制问题。我们提出了一个曲面上的最优系统，证明了解的存在唯一性，并分析了相关的有限元理论。为了减轻振荡现象，我们采用流线扩散稳定化方法。为了提高计算效率，以更少的自由度获得高分辨率的数值解，我们将流线扩散法与自适应网格细化相结合。最后，通过数值实验验证了该方法的优越性。

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 Numerical Mathematics 数学-应用数学

CiteScore

5.60

自引率

7.10%

发文量

225

审稿时长

7.2 months

期刊介绍： The purpose of the journal is to provide a forum for the publication of high quality research and tutorial papers in computational mathematics. In addition to the traditional issues and problems in numerical analysis, the journal also publishes papers describing relevant applications in such fields as physics, fluid dynamics, engineering and other branches of applied science with a computational mathematics component. The journal strives to be flexible in the type of papers it publishes and their format. Equally desirable are: (i) Full papers, which should be complete and relatively self-contained original contributions with an introduction that can be understood by the broad computational mathematics community. Both rigorous and heuristic styles are acceptable. Of particular interest are papers about new areas of research, in which other than strictly mathematical arguments may be important in establishing a basis for further developments. (ii) Tutorial review papers, covering some of the important issues in Numerical Mathematics, Scientific Computing and their Applications. The journal will occasionally publish contributions which are larger than the usual format for regular papers. (iii) Short notes, which present specific new results and techniques in a brief communication.