تقرير
Crouzeix-Raviart elements on simplicial meshes in $d$ dimensions
| العنوان: | Crouzeix-Raviart elements on simplicial meshes in $d$ dimensions |
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| المؤلفون: | Bohne, Nis-Erik, Ciarlet Jr., Patrick, Sauter, Stefan |
| سنة النشر: | 2024 |
| المجموعة: | Computer Science Mathematics |
| مصطلحات موضوعية: | Mathematics - Numerical Analysis, 33C45, 33C50, 65N30 (Primary) 65N12 (Secondary) |
| الوصف: | In this paper we introduce Crouzeix-Raviart elements of general polynomial order $k$ and spatial dimension $d\geq2$ for simplicial finite element meshes. We give explicit representations of the non-conforming basis functions and prove that the conforming companion space, i.e., the conforming finite element space of polynomial order $k$ is contained in the Crouzeix-Raviart space. We prove a direct sum decomposition of the Crouzeix-Raviart space into (a subspace of) the conforming companion space and the span of the non-conforming basis functions. Degrees of freedom are introduced which are bidual to the basis functions and give rise to the definition of a local approximation/interpolation operator. In two dimensions or for $k=1$, these freedoms can be split into simplex and $\left( d-1\right) $ dimensional facet integrals in such a way that, in a basis representation of Crouzeix-Raviart functions, all coefficients which belong to basis functions related to lower-dimensional faces in the mesh are determined by these facet integrals. It will also be shown that such a set of degrees of freedom does \textbf{not} exist in higher space dimension and $k>1$. Comment: 33 pages |
| نوع الوثيقة: | Working Paper |
| URL الوصول: | http://arxiv.org/abs/2407.04361 |
| رقم الأكسشن: | edsarx.2407.04361 |
| قاعدة البيانات: | arXiv |
| الوصف غير متاح. |