双变量等几何有限元空间在有退化角几何图形情况下的索波列夫正则性

IF 1.7 3区数学 Q2 MATHEMATICS, APPLIED Advances in Computational Mathematics Pub Date : 2024-10-24 DOI:10.1007/s10444-024-10203-x

Ulrich Reif

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引用次数: 0

摘要

我们研究了等几何分析中获得的双变量函数的 Sobolev 正则性，当使用几何映射时，这些几何映射是退化的，即第一偏导数在孤立点上消失。特别是，我们展示了已知的 D-patches 的 \(C^1\)-conditions 是如何被收紧以保证第二偏导数的平方可整性的，这在计算椭圆四阶 PDEs（如双谐方程）的有限元近似时是需要的。

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Sobolev regularity of bivariate isogeometric finite element spaces in case of a geometry map with degenerate corner

We investigate Sobolev regularity of bivariate functions obtained in Isogeometric Analysis when using geometry maps that are degenerate in the sense that the first partial derivatives vanish at isolated points. In particular, we show how the known \(C^1\)-conditions for D-patches have to be tightened to guarantee square integrability of second partial derivatives, as required when computing finite element approximations of elliptic fourth order PDEs like the biharmonic equation.

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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.