半线性抛物对流扩散问题的插值系数无稳定器弱 Galerkin 方法

IF 2.9 2区数学 Q1 MATHEMATICS, APPLIED

Applied Mathematics Letters Pub Date : 2024-08-13 DOI:10.1016/j.aml.2024.109268

Wenjuan Li , Fuzheng Gao , Jintao Cui

{"title":"半线性抛物对流扩散问题的插值系数无稳定器弱 Galerkin 方法","authors":"Wenjuan Li , Fuzheng Gao , Jintao Cui","doi":"10.1016/j.aml.2024.109268","DOIUrl":null,"url":null,"abstract":"<div><p>We continue our effort in Li et al. (2024) to explore an interpolated coefficients stabilizer-free weak Galerkin finite element method (IC SFWG-FEM) to solve a one-dimensional semilinear parabolic convection–diffusion equation. Due to the introduction of interpolated coefficients and the design without stabilizers, this method not only possesses the capability of approximating functions and sparsity in the stiffness matrix, but also reduces the complexity of analysis and programming. Theoretical analysis of stability for the semi-discrete IC SFWG finite element scheme is provided. Moreover, numerical experiments are carried out to demonstrate the effectivity and stability.</p></div>","PeriodicalId":55497,"journal":{"name":"Applied Mathematics Letters","volume":"159 ","pages":"Article 109268"},"PeriodicalIF":2.9000,"publicationDate":"2024-08-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Interpolated coefficients stabilizer-free weak Galerkin method for semilinear parabolic convection–diffusion problem\",\"authors\":\"Wenjuan Li , Fuzheng Gao , Jintao Cui\",\"doi\":\"10.1016/j.aml.2024.109268\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>We continue our effort in Li et al. (2024) to explore an interpolated coefficients stabilizer-free weak Galerkin finite element method (IC SFWG-FEM) to solve a one-dimensional semilinear parabolic convection–diffusion equation. Due to the introduction of interpolated coefficients and the design without stabilizers, this method not only possesses the capability of approximating functions and sparsity in the stiffness matrix, but also reduces the complexity of analysis and programming. Theoretical analysis of stability for the semi-discrete IC SFWG finite element scheme is provided. Moreover, numerical experiments are carried out to demonstrate the effectivity and stability.</p></div>\",\"PeriodicalId\":55497,\"journal\":{\"name\":\"Applied Mathematics Letters\",\"volume\":\"159 \",\"pages\":\"Article 109268\"},\"PeriodicalIF\":2.9000,\"publicationDate\":\"2024-08-13\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Applied Mathematics Letters\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://www.sciencedirect.com/science/article/pii/S089396592400288X\",\"RegionNum\":2,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"MATHEMATICS, APPLIED\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Applied Mathematics Letters","FirstCategoryId":"100","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S089396592400288X","RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}

引用次数: 0

摘要

我们继续 Li 等人（2024）的努力，探索一种内插系数无稳定器弱 Galerkin 有限元方法（IC SFWG-FEM）来求解一维半线性抛物对流扩散方程。由于引入了插值系数和无稳定器设计，该方法不仅具有近似函数和刚度矩阵稀疏性的能力，还降低了分析和编程的复杂性。本文对半离散集成电路 SFWG 有限元方案的稳定性进行了理论分析。此外，还进行了数值实验来证明其有效性和稳定性。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

查看原文本刊更多论文

Interpolated coefficients stabilizer-free weak Galerkin method for semilinear parabolic convection–diffusion problem

We continue our effort in Li et al. (2024) to explore an interpolated coefficients stabilizer-free weak Galerkin finite element method (IC SFWG-FEM) to solve a one-dimensional semilinear parabolic convection–diffusion equation. Due to the introduction of interpolated coefficients and the design without stabilizers, this method not only possesses the capability of approximating functions and sparsity in the stiffness matrix, but also reduces the complexity of analysis and programming. Theoretical analysis of stability for the semi-discrete IC SFWG finite element scheme is provided. Moreover, numerical experiments are carried out to demonstrate the effectivity and stability.

求助全文

通过发布文献求助，成功后即可免费获取论文全文。去求助

来源期刊

Applied Mathematics Letters 数学-应用数学

CiteScore

7.70

自引率

5.40%

发文量

347

审稿时长

10 days

期刊介绍： The purpose of Applied Mathematics Letters is to provide a means of rapid publication for important but brief applied mathematical papers. The brief descriptions of any work involving a novel application or utilization of mathematics, or a development in the methodology of applied mathematics is a potential contribution for this journal. This journal''s focus is on applied mathematics topics based on differential equations and linear algebra. Priority will be given to submissions that are likely to appeal to a wide audience.