四面体网格上不一致P3+B4和不连续P2混合有限元

IF 2.1 3区数学 Q2 MATHEMATICS, APPLIED

Advances in Computational Mathematics Pub Date : 2025-06-23 DOI:10.1007/s10444-025-10244-w

Xuejun Xu, Shangyou Zhang

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引用次数: 0

摘要

通过在每个四面体上用9个P4P_4不一致气泡丰富符合p3p3有限元空间，构造了一个不符合p3p3有限元。这里，P4P_4泡的散度不是P3P_3多项式，而是P2P_2多项式。这种不一致的P3P_3有限元与不连续的P2P_2有限元相结合，对一般四面体网格上的Stokes方程具有不稳定的解。因此，这种混合有限元方法可以得到求解平稳Stokes方程的准最优解。对于这些特殊的P4P_4气泡，离散速度保持局部无点发散。数值试验证实了这一理论。

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A nonconforming P3+B4 and discontinuous P2 mixed finite element on tetrahedral grids

A nonconforming \(P_3\) finite element is constructed by enriching the conforming \(P_3\) finite element space with nine \(P_4\) nonconforming bubbles, on each tetrahedron. Here, the divergence of the \(P_4\) bubble is not a \(P_3\) polynomial, but a \(P_2\) polynomial. This nonconforming \(P_3\) finite element, combined with the discontinuous \(P_2\) finite element, is inf-sup stable for solving the Stokes equations on general tetrahedral grids. Consequently, such a mixed finite element method produces quasi-optimal solutions for solving the stationary Stokes equations. With these special \(P_4\) bubbles, the discrete velocity remains locally pointwise divergence-free. Numerical tests confirm the theory.

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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.