Related papers: Crouzeix-Raviart elements on simplicial meshes in …
In this paper, we prove that Crouzeix-Raviart finite elements of polynomial order $p\geq5$, $p$ odd, are inf-sup stable for the Stokes problem on triangulations. For $p\geq4$, $p$ even, the stability was proved by \'{A}. Baran and G. Stoyan…
The construction of $C^m$ conforming finite elements on simplicial meshes has recently advanced through the groundbreaking work of Hu, Lin, and Wu (Found. Comput. Math. 24, 2024). Their framework characterizes smoothness via moments of…
We examine the dimensions of various inf-sup stable mixed finite element spaces on tetrahedral meshes in 3D with exact divergence constraints. More precisely, we compare the standard Scott-Vogelius elements of higher polynomial degree and…
We develop a family of finite element spaces of differential forms defined on cubical meshes in any number of dimensions. The family contains elements of all polynomial degrees and all form degrees. In two dimensions, these include the…
In this paper, a new method is proposed to produce guaranteed lower bounds for eigenvalues of general second order elliptic operators in any dimension. Unlike most methods in the literature, the proposed method only needs to solve one…
Finite element spaces by Whitney $k$-forms on cubical meshes in $\mathbb{R}^n$ are presented. Based on the spaces, compatible discretizations to $H\Lambda^k$ problems are provided, and discrete de Rham complexes and commutative diagrams are…
The purpose of the present paper is to develop $C^1$ Virtual Elements in three dimensions for linear elliptic fourth order problems, motivated by the difficulties that standard conforming Finite Elements encounter in this framework. We…
Holomorphic fields play an important role in 2d conformal field theory. We generalize them to d>2 by introducing the notion of Cauchy conformal fields, which satisfy a first order differential equation such that they are determined…
We introduce the family of trimmed serendipity finite element differential form spaces, defined on cubical meshes in any number of dimensions, for any polynomial degree, and for any form order. The relation between the trimmed serendipity…
This paper analyses conforming and nonconforming virtual element formulations of arbitrary polynomial degrees on general polygonal meshes for the coupling of solid and fluid phases in deformable porous plates. The governing equations…
This work establishes the well-posedness and a priori error analysis for the mixed FEEC-type finite element approximation of the three-dimensional vector Laplace boundary value problem subject to the Dirichlet boundary condition. The…
In this paper, we present two variants of the Additive Schwarz Method for a Crouzeix-Raviart finite volume element (CRFVE) discretization of second order elliptic problems with discontinuous coefficients where the discontinuities are only…
We consider the approximation properties of finite element spaces on quadrilateral meshes. The finite element spaces are constructed starting with a given finite dimensional space of functions on a square reference element, which is then…
We derive a discrete $ L^q-L^p$ Sobolev inequality tailored for the Crouzeix--Raviart and discontinuous Crouzeix--Raviart finite element spaces on anisotropic meshes in both two and three dimensions. Subject to a semi-regular mesh…
In this paper we present a novel arbitrary-order discrete de Rham (DDR) complex on general polyhedral meshes based on the decomposition of polynomial spaces into ranges of vector calculus operators and complements linked to the spaces in…
In this paper, three high-accuracy methods for eigenvalues of second order elliptic operators are proposed by using the nonconforming Crouzeix-Raviart(CR for short) element and the nonconforming enriched Crouzeix-Raviart(ECR for short)…
Several div-conforming and divdiv-conforming finite elements for symmetric tensors on simplexes in arbitrary dimension are constructed in this work. The shape function space is first split as the trace space and the bubble space. The later…
New low-order $H(\textrm{div})$-conforming finite elements for symmetric tensors are constructed in arbitrary dimension. The space of shape functions is defined by enriching the symmetric quadratic polynomial space with the $(d+1)$-order…
Discrete de Rham (DDR) methods provide non-conforming but compatible approximations of the continuous de Rham complex on general polytopal meshes. Owing to the non-conformity, several challenges arise in the analysis of these methods. In…
A family of mixed finite elements is proposed for solving the first order system of linear elasticity equations in any space dimension, where the stress field is approximated by symmetric finite element tensors. This family of elements has…