H（旋度）和H（div）平流问题的局部投影镇定方法

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.2025.117129

Yangfan Luo , Jindong Wang , Shuonan Wu

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引用次数: 0

摘要

我们设计了局部投影稳定（LPS）方法在H（旋度）和H（div）空间的平流问题，采用统一框架内任意阶的一致性有限元空间。关键因素是一个局部的辅助条件，通过用适当的H(d)泡函数（d = curl或div）丰富近似空间来实现。这种丰富允许构造一个改进的插值算子，这对于在能量范数中建立最优先验误差估计至关重要。数值算例验证了该方法的理论结果和稳定性。

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Local projection stabilization methods for H(curl) and H(div) advection problems

We devise local projection stabilization (LPS) methods for advection problems in the

H

(curl) and

H

(div) spaces, employing conforming finite element spaces of arbitrary order within a unified framework. The key ingredient is a local inf–sup condition, enabled by enriching the approximation space with appropriate

H

(d) bubble functions (with d

=

curl or div). This enrichment allows for the construction of a modified interpolation operator, which is crucial for establishing optimal a priori error estimates in the energy norm. Numerical examples are presented to verify both the theoretical results and the stabilization properties of the proposed method.

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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.