Finite Element Approximation for the Delayed Generalized Burgers–Huxley Equation with Weakly Singular Kernel: Part II Nonconforming and DG Approximation

IF 3 2区数学 Q1 MATHEMATICS, APPLIED

SIAM Journal on Scientific Computing Pub Date : 2024-09-19 DOI:10.1137/23m1612196

Sumit Mahahjan, Arbaz Khan

引用次数: 0

Abstract

SIAM Journal on Scientific Computing, Volume 46, Issue 5, Page A2972-A2998, October 2024.
Abstract. In this paper, the numerical approximation of the generalized Burgers–Huxley equation (GBHE) with weakly singular kernels using nonconforming methods will be presented. Specifically, we discuss two new formulations. The first formulation is based on the nonconforming finite element method. The other formulation is based on discontinuous Galerkin finite element methods. The wellposedness results for both formulations are proved. Then, a priori error estimates for both the semidiscrete and fully discrete schemes are derived. Specific numerical examples, including some applications for the GBHE with a weakly singular model, are discussed to validate the theoretical results.

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具有弱奇异内核的延迟广义伯格斯-赫胥黎方程的有限元近似：第二部分不符和 DG 近似算法

SIAM 科学计算期刊》，第 46 卷第 5 期，第 A2972-A2998 页，2024 年 10 月。摘要本文将介绍使用非符合方法对具有弱奇异内核的广义伯格斯-赫胥黎方程（GBHE）进行数值逼近。具体来说，我们讨论了两种新的公式。第一种公式是基于不拘泥有限元法。另一种公式基于非连续 Galerkin 有限元方法。我们证明了这两种公式的拟合结果。然后，得出了半离散和完全离散方案的先验误差估计。讨论了具体的数值示例，包括一些弱奇异模型 GBHE 的应用，以验证理论结果。

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

SIAM Journal on Scientific Computing 数学-应用数学

CiteScore

5.50

自引率

3.20%

发文量

209

审稿时长

1 months

期刊介绍： The purpose of SIAM Journal on Scientific Computing (SISC) is to advance computational methods for solving scientific and engineering problems. SISC papers are classified into three categories: 1. Methods and Algorithms for Scientific Computing: Papers in this category may include theoretical analysis, provided that the relevance to applications in science and engineering is demonstrated. They should contain meaningful computational results and theoretical results or strong heuristics supporting the performance of new algorithms. 2. Computational Methods in Science and Engineering: Papers in this section will typically describe novel methodologies for solving a specific problem in computational science or engineering. They should contain enough information about the application to orient other computational scientists but should omit details of interest mainly to the applications specialist. 3. Software and High-Performance Computing: Papers in this category should concern the novel design and development of computational methods and high-quality software, parallel algorithms, high-performance computing issues, new architectures, data analysis, or visualization. The primary focus should be on computational methods that have potentially large impact for an important class of scientific or engineering problems.