曲面上一般二阶椭圆问题的非协调虚元法

IF 2.1 3区数学 Q2 MATHEMATICS, APPLIED

Advances in Computational Mathematics Pub Date : 2025-07-04 DOI:10.1007/s10444-025-10242-y

Yi Liu, Alessandro Russo

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引用次数: 0

摘要

L. beir o da Veiga， Y. Liu， L. Mascotto， A. Russo等（J. Sci.）提出并分析了带曲面边的Poisson方程非协调虚元法。计算。99(1)2024)。本文的目的是将非协调虚元法推广到具有弯曲边界和弯曲内界面域的更一般的二阶变系数椭圆问题。在一组多边形网格上通过数值实验证明了该方法在能量和L2L^2范数上具有任意阶的最优收敛性。该方法所提供的数值近似精度与理论分析结果相当。

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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Nonconforming virtual element method for general second-order elliptic problems on curved domain

The nonconforming virtual element method with curved edges was proposed and analyzed for the Poisson equation by L. Beirão da Veiga, Y. Liu, L. Mascotto, and A. Russo in (J. Sci. Comput. 99(1) 2024). The goal of this paper is to extend the nonconforming virtual element method to a more general second-order elliptic problem with variable coefficients in domains with curved boundaries and curved internal interfaces. We prove an optimal convergence of arbitrary order in the energy and \(L^2\)-norms, confirmed by numerical experiments on a set of polygonal meshes. The accuracy of the numerical approximation provided by the method is shown to be comparable with that obtained from the theoretical analysis.

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来源期刊

Advances in Computational Mathematics 数学-应用数学

CiteScore

3.00

自引率

5.90%

发文量

审稿时长

3 months

期刊介绍： Advances in Computational Mathematics publishes high quality, accessible and original articles at the forefront of computational and applied mathematics, with a clear potential for impact across the sciences. The journal emphasizes three core areas: approximation theory and computational geometry; numerical analysis, modelling and simulation; imaging, signal processing and data analysis. This journal welcomes papers that are accessible to a broad audience in the mathematical sciences and that show either an advance in computational methodology or a novel scientific application area, or both. Methods papers should rely on rigorous analysis and/or convincing numerical studies.