تقرير
Nonlinear elasticity complex and a finite element diagram chase
| العنوان: | Nonlinear elasticity complex and a finite element diagram chase |
|---|---|
| المؤلفون: | Hu, Kaibo |
| سنة النشر: | 2023 |
| المجموعة: | Computer Science Mathematics |
| مصطلحات موضوعية: | Mathematics - Numerical Analysis |
| الوصف: | In this paper, we present a nonlinear version of the linear elasticity (Calabi, Kr\"oner, Riemannian deformation) complex which encodes isometric embedding, metric, curvature and the Bianchi identity. We reformulate the rigidity theorem and a fundamental theorem of Riemannian geometry as the exactness of this complex. Then we generalize an algebraic approach for constructing finite elements for the Bernstein-Gelfand-Gelfand (BGG) complexes. In particular, we discuss the reduction of degrees of freedom with injective connecting maps in the BGG diagrams. We derive a strain complex in two space dimensions with a diagram chase. Comment: Manuscript prepared for proceedings of the INdAM conference "Approximation Theory and Numerical Analysis meet Algebra, Geometry, Topology'', which was held in September 2022 at Cortona, Italy |
| نوع الوثيقة: | Working Paper |
| URL الوصول: | http://arxiv.org/abs/2302.02442 |
| رقم الأكسشن: | edsarx.2302.02442 |
| قاعدة البيانات: | arXiv |
| الوصف غير متاح. |