Related papers: Novel $H^\mathrm{dev}(\mathrm{Curl})$-conforming e…
Based on a new H$^2-$Korn's inequality, we propose new nonconforming elements for the linear strain gradient elastic model. The first group of elements are H$^1-$conforming but H$^2-$nonconforming. The tensor product NTW element [Tai:2001]…
We provide an adaptive finite element approximation for a model of quasi-static crack growth in dimension two. The discrete setting consists of integral functionals that are defined on continuous, piecewise affine functions, where the…
In this paper we consider the equilibrium problem in the relaxed linear model of micromorphic elastic materials. The basic kinematical fields of this extended continuum model are the displacement $u\in \mathbb{R}^3$ and the non-symmetric…
In this work, we study a primal hybrid finite element method for the approximation of linear elasticity problems, posed in terms of displacement, an auxiliary pressure field, and a Lagrange multiplier related to the traction. We develop a…
A unified construction of $H(\textrm{div})$-conforming finite element tensors, including vector element, symmetric matrix element, traceless matrix element, and, in general, tensors with linear constraints, is developed in this work. It is…
In this paper, we develop two fully nonconforming (both H(grad curl)-nonconforming and H(curl)-nonconforming) finite elements on cubical meshes which can fit into the Stokes complex. The newly proposed elements have 24 and 36 degrees of…
We develop a method to compute $H^2$-conforming finite element approximations in both two and three space dimensions using readily available finite element spaces. This is accomplished by deriving a novel, equivalent mixed variational…
A conforming triangular mixed element recently proposed by Hu and Zhang for linear elasticity is extended by rearranging the global degrees of freedom. More precisely, adaptive meshes $\mathcal{T}_1$, $\cdots$, $\mathcal{T}_N$ which are…
Finite element approximation to a decoupled formulation for the quad--curl problem is studied in this paper. The difficulty of constructing elements with certain conformity to the quad--curl problems has been greatly reduced. For convex…
We introduce a dense and a dilute loop model on causal dynamical triangulations. Both models are characterised by a geometric coupling constant $g$ and a loop parameter $\alpha$ in such a way that the purely geometric causal triangulation…
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…
A robust $hp$-adaptive finite element framework is presented for the investigation of static cracks in materials characterized by complex, pointwise density variations. Within such heterogeneous media, the equilibrium equation governed by…
The classical continuous mixed formulation of linear elasticity with pointwise symmetric stresses allows for a conforming finite element discretization with piecewise polynomials of degree at least three. Symmetric stress approximations of…
Two types of finite element spaces on triangles are constructed for div-div conforming symmetric tensors. Besides the normal-normal continuity, the stress tensor is continuous at vertices and another trace involving combination of…
The wide adoption of thermoplastic composites to reduce weight in structural parts requires reliable numerical methods to account for debonding between overmolded parts. Although cohesive elements are effective for debonding, the need for…
Conforming hexahedral (hex) meshes are favored in simulation for their superior numerical properties, yet automatically decomposing a general 3D volume into a conforming hex mesh remains a formidable challenge. Among existing approaches,…
We analyze finite element discretizations of scalar curvature in dimension $N \ge 2$. Our analysis focuses on piecewise polynomial interpolants of a smooth Riemannian metric $g$ on a simplicial triangulation of a polyhedral domain $\Omega…
This paper constructs a unified family of nonconforming finite element spaces for $H\Lambda^k$ in $\mathbb{R}^n$ ($0\leqslant k\leqslant n$, $n\geqslant 1$). The spaces employ piecewise Whitney forms as shape functions, and include the…
Parametric finite element discretizations of constrained geometric flows must simultaneously address high-order geometric stiffness, mesh degeneration, and nonlinear global constraints. This paper develops a stabilized dual-SAV (scalar…
We develop a finite element discretization for the weakly symmetric equations of linear elasticity on tetrahedral meshes. The finite element combines, for $r \geq 0$, discontinuous polynomials of $r$ for the displacement,…