Higher-degree rectangular immersed finite elements discontinuous Galerkin methods for elliptic interface problems

IF 2.6 2区数学 Q1 MATHEMATICS, APPLIED

Journal of Computational and Applied Mathematics Pub Date : 2025-10-03 DOI:10.1016/j.cam.2025.117126

Qiao Zhuang , Zhongqiang Zhang , Marcus Sarkis , Tao Lin

引用次数: 0

Abstract

We propose and analyze higher-degree rectangular immersed finite elements (IFE) for elliptic interface problems. These IFE functions are constructed by a Cauchy extension. Properties of the proposed IFE functions are analyzed, including the optimal approximation capability of the resulting IFE spaces, as well as inverse and trace inequalities. The higher-degree rectangular IFE spaces are employed in discontinuous Galerkin (DG) formulations to solve the elliptic interface problems. The optimal error estimates for the proposed DGIFE methods in both an energy and

L^{2}

norms are derived. Numerical results are provided to illustrate the convergence of the proposed DGIFE methods.

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椭圆界面问题的高次矩形浸入有限元不连续伽辽金法

针对椭圆界面问题，提出并分析了高次矩形浸没有限元。这些IFE函数是由柯西扩展构造的。分析了所提出的IFE函数的性质，包括所得到的IFE空间的最优逼近能力，以及逆不等式和迹不等式。在不连续Galerkin （DG）公式中，采用了高次矩形IFE空间求解椭圆界面问题。给出了该方法在能量范数和L2范数下的最优误差估计。数值结果说明了所提DGIFE方法的收敛性。

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

Journal of Computational and Applied Mathematics 数学-应用数学

CiteScore

5.40

自引率

4.20%

发文量

437

审稿时长

3.0 months

期刊介绍： The Journal of Computational and Applied Mathematics publishes original papers of high scientific value in all areas of computational and applied mathematics. The main interest of the Journal is in papers that describe and analyze new computational techniques for solving scientific or engineering problems. Also the improved analysis, including the effectiveness and applicability, of existing methods and algorithms is of importance. The computational efficiency (e.g. the convergence, stability, accuracy, ...) should be proved and illustrated by nontrivial numerical examples. Papers describing only variants of existing methods, without adding significant new computational properties are not of interest. The audience consists of: applied mathematicians, numerical analysts, computational scientists and engineers.