A unified space-time finite element scheme for a quasilinear parabolic problem

IF 2.4 2区数学 Q1 MATHEMATICS, APPLIED

Applied Numerical Mathematics Pub Date : 2025-04-02 DOI:10.1016/j.apnum.2025.03.006

I. Toulopoulos

引用次数: 0

Abstract

A new approach is presented to obtain stabilized space - time finite element schemes for solving in a unified space-time way a quasilinear parabolic model problem. The procedure consists in introducing first upwind diffusion terms with an appropriate scaling factor in the initial space-time finite element scheme. Then additional interface jump terms are introduced for ensuring the consistency of the final finite element discetzation. A discretization error analysis is presented and a priori error estimates in an appropriate discrete norm are shown. The corresponding convergence rates are optimal with respect to the regularity of the solution and are confirmed through a series of numerical tests.

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拟线性抛物问题的统一时空有限元格式

提出了一种以统一时空方式求解拟线性抛物模型问题的稳定时空有限元格式的新方法。该过程包括在初始时空有限元格式中引入具有适当比例因子的第一逆风扩散项。为了保证最终有限元剖分结果的一致性，引入了附加的界面跳跃项。给出了离散化误差分析，并给出了在适当的离散范数下的先验误差估计。相应的收敛速率相对于解的正则性是最优的，并通过一系列数值试验得到了证实。

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.