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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…

Numerical Analysis · Mathematics 2025-10-20 Douglas N. Arnold , Daniele Boffi , Richard S. Falk

We continue the investigation on the spectrum of operators arising from the discretization of partial differential equations. In this paper we consider a three field formulation recently introduced for the finite element least-squares…

Numerical Analysis · Mathematics 2021-08-19 Linda Alzaben , Daniele Boffi

This paper extends the Bernstein-Gelfand-Gelfand (BGG) framework to the construction of finite element conformal Hessian complexes and conformal elasticity complexes in three dimensions involving conformal tensors (i.e., symmetric and…

Numerical Analysis · Mathematics 2025-08-07 Xuehai Huang

A new family of locking-free finite elements for shear deformable Reissner-Mindlin plates is presented. The elements are based on the "tangential-displacement normal-normal-stress" formulation of elasticity. In this formulation, the bending…

Numerical Analysis · Mathematics 2018-07-31 Astrid Pechstein , Joachim Schöberl

We investigate a finite element discretization of an elastic bending-plate model with an effective prestrain. The model has been obtained via homogenization and dimension reduction by B\"onlein at al. (2023). Its energy functional is the…

Numerical Analysis · Mathematics 2025-10-13 Klaus Böhnlein , Stefan Neukamm , Oliver Sander

A finite element approach for approximating the solution of a mathematical model for the response of a penetrable, bounded object (obstacle) to the excitation by an external electromagnetic field is presented and investigated. The model…

Numerical Analysis · Mathematics 2026-04-16 Lutz Angermann

Two non-overlapping domain decomposition methods are presented for the mixed finite element formulation of linear elasticity with weakly enforced stress symmetry. The methods utilize either displacement or normal stress Lagrange multiplier…

Numerical Analysis · Mathematics 2017-11-28 Eldar Khattatov , Ivan Yotov

We construct a cut finite element method for the membrane elasticity problem on an embedded mesh using tangential differential calculus. Both free membranes and membranes coupled to 3D elasticity are considered. The discretization comes…

Numerical Analysis · Mathematics 2016-08-24 Mirza Cenanovic , Peter Hansbo , Mats G. Larson

The proposed two-dimensional geometrically exact beam element extends our previous work by including the effects of shear distortion, and also of distributed forces and moments acting along the beam. The general flexibility-based…

Numerical Analysis · Mathematics 2025-08-06 Milan Jirasek , Martin Horak , Emma La Malfa Ribolla , Chiara Bonvissuto

Within the framework of finite element systems, we show how spaces of differential forms may be constructed, in such a way that they are equipped with commuting interpolators and contain prescribed functions, and are minimal under these…

Numerical Analysis · Mathematics 2015-10-22 Snorre H. Christiansen , Andrew Gillette

This paper presents a novel exact finite element formulation of quasi-3D beam for high-fidelity analysis of functionally graded sandwich beams. Unlike conventional displacement-based elements that rely on approximate interpolation functions…

Numerical Analysis · Mathematics 2026-01-21 Wenxiong Li , Suiyin Chen

A first-order system least squares formulation for the sea-ice dynamics is presented. In addition to the displacement field, the stress tensor is used as a variable. As finite element spaces, standard conforming piecewise polynomials for…

Numerical Analysis · Mathematics 2018-09-06 Fleurianne Bertrand

This paper considers the coupled problem of a three-dimensional elastic body and a two-dimensional plate, which are rigidly connected at their interface. The plate consists of a plane elasticity model along the longitudinal direction and a…

Numerical Analysis · Mathematics 2025-09-16 Jun Hu , Zhen Liu , Rui Ma

A family of conforming virtual element Hessian complexes on tetrahedral meshes are constructed based on decompositions of polynomial tensor spaces. They are applied to discretize the linearized time-independent Einstein-Bianchi system with…

General Relativity and Quantum Cosmology · Physics 2025-06-10 Long Chen , Xuehai Huang

We develop a Nitsche finite element method for a model of Euler--Bernoulli beams with axial stiffness embedded in a two--dimensional elastic bulk domain. The beams have their own displacement fields, and the elastic subdomains created by…

Numerical Analysis · Mathematics 2022-03-02 Peter Hansbo , Mats G. Larson

In this article we consider the linear elasticity problem in an axisymmetric three dimensional domain, with data which are axisymmetric and have zero angular component. The weak formulation of the the three dimensional problem reduces to a…

Numerical Analysis · Mathematics 2020-12-30 Alistair Bentley , V. J. Ervin

With the development of multi-layer elastic systems in the field of engineering mechanics, the corresponding variational inequality theory and algorithm design have received more attention and research. In this study, a class of equivalent…

Numerical Analysis · Mathematics 2024-09-11 Zhizhuo Zhang , Mikaël Barboteu , Xiaobing Nie , Serge Dumont , Mahmoud Abdel-Aty , Jinde Cao

We present a class of discretisation spaces and H(div)-conformal elements that can be built on any polytope. Bridging the flexibility of the Virtual Element spaces towards the element's shape with the divergence properties of the…

Numerical Analysis · Mathematics 2019-07-23 Rémi Abgrall , Élise Le Mélédo , Philipp Öffner

In this paper, we present a family of new mixed finite element methods for linear elasticity for both spatial dimensions $n=2,3$, which yields a conforming and strongly symmetric approximation for stress. Applying…

Numerical Analysis · Mathematics 2017-04-26 Shihua Gong , Shuonan Wu , Jinchao Xu

Interpolation methods for nonlinear finite element discretizations are commonly used to eliminate the computational costs associated with the repeated assembly of the nonlinear systems. While the group finite element formulation…

Numerical Analysis · Mathematics 2020-09-24 Kevin Tolle , Nicole Marheineke