涉及梯度丰富连续体混合物问题的先验误差分析

IF 1.3 4区数学 Q1 MATHEMATICS International Journal of Numerical Analysis and Modeling Pub Date : 2024-04-01 DOI:10.4208/ijnam2024-1006

Noelia Bazarra,José R. Fernández,Antonio Magaña,Marc Magaña, Ramόn Quintanilla

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引用次数: 0

摘要

在这项工作中，我们研究了一个涉及混合物的应变梯度问题。变分公式被写成抛物线变分方程的一阶时间耦合系统。然后，我们利用有限元法和隐式欧拉方案引入了完全离散的近似方法。证明了离散稳定性和先验误差估计。最后，进行了一些一维和二维数值模拟。

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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An a Priori Error Analysis of a Problem Involving Mixtures of Continua with Gradient Enrichment

In this work, we study a strain gradient problem involving mixtures. The variational formulation is written as a first-order in time coupled system of parabolic variational equations. An existence and uniqueness result is recalled. Then, we introduce a fully discrete approximation by using the finite element method and the implicit Euler scheme. A discrete stability property and a priori error estimates are proved. Finally, some one- and two-dimensional numerical simulations are performed.

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来源期刊

International Journal of Numerical Analysis and Modeling 数学-数学

CiteScore

2.10

自引率

9.10%

发文量

审稿时长

6-12 weeks

期刊介绍： The journal is directed to the broad spectrum of researchers in numerical methods throughout science and engineering, and publishes high quality original papers in all fields of numerical analysis and mathematical modeling including: numerical differential equations, scientific computing, linear algebra, control, optimization, and related areas of engineering and scientific applications. The journal welcomes the contribution of original developments of numerical methods, mathematical analysis leading to better understanding of the existing algorithms, and applications of numerical techniques to real engineering and scientific problems. Rigorous studies of the convergence of algorithms, their accuracy and stability, and their computational complexity are appropriate for this journal. Papers addressing new numerical algorithms and techniques, demonstrating the potential of some novel ideas, describing experiments involving new models and simulations for practical problems are also suitable topics for the journal. The journal welcomes survey articles which summarize state of art knowledge and present open problems of particular numerical techniques and mathematical models.