无稳定器多边形和多面体虚元

IF 2.3 2区数学 Q1 MATHEMATICS, APPLIED

Applied Numerical Mathematics Pub Date : 2026-02-01 Epub Date: 2025-10-25 DOI:10.1016/j.apnum.2025.10.015

Yanping Lin , Shangyou Zhang

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引用次数: 0

摘要

无稳定器Pk虚元分别在多边形和多面体网格上构造。这里的插值空间是每个多边形的三角形细分或每个多面体的四面体细分上的连续Pk多项式的空间。通过这种精确、合理的插补，消除了虚元的稳定器，保证了系统的正定。证明了无稳定器虚元在二维和三维中收敛于最优阶。算例验证了理论的正确性。

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Stabilizer-free polygonal and polyhedral virtual elements

Stabilizer-free

P_{k}

virtual elements are constructed on polygonal and polyhedral meshes. Here the interpolating space is the space of continuous

P_{k}

polynomials on a triangular-subdivision of each polygon, or a tetrahedral-subdivision of each polyhedron. With such an accurate and proper interpolation, the stabilizer of the virtual elements is eliminated while the system is kept positive-definite. We show that the stabilizer-free virtual elements converge at the optimal order in 2D and 3D. Numerical examples are computed, validating the theory.

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来源期刊

Applied Numerical Mathematics 数学-应用数学

CiteScore

5.60

自引率

7.10%

发文量

225

审稿时长

7.2 months

期刊介绍： The purpose of the journal is to provide a forum for the publication of high quality research and tutorial papers in computational mathematics. In addition to the traditional issues and problems in numerical analysis, the journal also publishes papers describing relevant applications in such fields as physics, fluid dynamics, engineering and other branches of applied science with a computational mathematics component. The journal strives to be flexible in the type of papers it publishes and their format. Equally desirable are: (i) Full papers, which should be complete and relatively self-contained original contributions with an introduction that can be understood by the broad computational mathematics community. Both rigorous and heuristic styles are acceptable. Of particular interest are papers about new areas of research, in which other than strictly mathematical arguments may be important in establishing a basis for further developments. (ii) Tutorial review papers, covering some of the important issues in Numerical Mathematics, Scientific Computing and their Applications. The journal will occasionally publish contributions which are larger than the usual format for regular papers. (iii) Short notes, which present specific new results and techniques in a brief communication.