Discrete tensor product BGG sequences: Splines and finite elements

IF 4.6 Q2 MATERIALS SCIENCE, BIOMATERIALS

ACS Applied Bio Materials Pub Date : 2024-04-17 DOI:10.1090/mcom/3969

F. Bonizzoni, Kaibo Hu, Guido Kanschat, Duygu Sap

引用次数: 0

Abstract

In this paper, we provide a systematic discretization of the Bernstein-Gelfand-Gelfand diagrams and complexes over cubical meshes in arbitrary dimension via the use of tensor product structures of one-dimensional piecewise-polynomial spaces, such as spline and finite element spaces. We demonstrate the construction of the Hessian, the elasticity, and div ⁡ div \operatorname {div}\operatorname {div} complexes as examples for our construction.

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离散张量积 BGG 序列：样条曲线和有限元

在本文中，我们通过使用一维片状多项式空间的张量乘结构（如样条空间和有限元空间），对任意维度立方网格上的伯恩斯坦-格尔芬-格尔芬图和复数进行了系统离散化。我们以 Hessian、弹性和 div div \operatorname {div}\operatorname {div} 复数的构造为例，演示了我们的构造。

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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来源期刊

ACS Applied Bio Materials Chemistry-Chemistry (all)

CiteScore

9.40

自引率

2.10%

发文量

464

期刊介绍： ACS Applied Bio Materials is an interdisciplinary journal publishing original research covering all aspects of biomaterials and biointerfaces including and beyond the traditional biosensing, biomedical and therapeutic applications. The journal is devoted to reports of new and original experimental and theoretical research of an applied nature that integrates knowledge in the areas of materials, engineering, physics, bioscience, and chemistry into important bio applications. The journal is specifically interested in work that addresses the relationship between structure and function and assesses the stability and degradation of materials under relevant environmental and biological conditions.