具有运动界面的平流扩散问题的拟合时空有限元方法

IF 2.2 2区数学 Q1 MATHEMATICS, APPLIED

Applied Numerical Mathematics Pub Date : 2025-01-09 DOI:10.1016/j.apnum.2025.01.002

Quang Huy Nguyen , Van Chien Le , Phuong Cuc Hoang , Thi Thanh Mai Ta

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引用次数: 0

摘要

本文提出了求解具有非平稳界面的抛物型平流扩散问题的一种拟合时空界面的有限元方法。扩散系数的跳跃导致溶液梯度在界面上的不连续。利用Banach-Nečas-Babuška定理证明了连续变分问题的适定性。采用伽辽金法和非结构化界面拟合网格，分析了一种基于全离散有限元的方案。在全局低而局部高正则性条件下，建立了离散能量范数的最优误差估计。一些数值结果证实了我们的理论结果。

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A fitted space-time finite element method for an advection-diffusion problem with moving interfaces

This paper presents a space-time interface-fitted finite element method for solving a parabolic advection-diffusion problem with a nonstationary interface. The jumping diffusion coefficient gives rise to the discontinuity of the solution gradient across the interface. We use the Banach-Nečas-Babuška theorem to show the well-posedness of the continuous variational problem. A fully discrete finite-element based scheme is analyzed using the Galerkin method and unstructured interface-fitted meshes. An optimal error estimate is established in a discrete energy norm under a globally low but locally high regularity condition. Some numerical results corroborate our theoretical results.

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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.