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We construct conforming finite element elasticity complexes on Worsey-Farin splits in three dimensions. Spaces for displacement, strain, stress, and the load are connected in the elasticity complex through the differential operators…

Numerical Analysis · Mathematics 2023-08-22 Sining Gong , Jay Gopalakrishnan , Johnny Guzmán , Michael Neilan

We present a virtual element method for the Reissner-Mindlin plate bending problem which uses shear strain and deflection as discrete variables without the need of any reduction operator. The proposed method is conforming in…

Numerical Analysis · Mathematics 2018-10-23 Lourenço Beirão da Veiga , David Mora , Gonzalo Rivera

We analyze the application to elastodynamic problems of mixed finite element methods for elasticity with weak symmetry. Our approach leads to a semidiscrete method which consists of a system of ordinary differential equations without…

Numerical Analysis · Mathematics 2018-11-13 Douglas N. Arnold , Jeonghun J. Lee

Several physical problems modeled by second-order elliptic equations can be efficiently solved using mixed finite elements of the Raviart-Thomas family RTk for N-simplexes, introduced in the seventies. In case Neumann conditions are…

Numerical Analysis · Mathematics 2025-04-01 Fleurianne Bertrand , Vitoriano Ruas

The multiscale hybrid-mixed (MHM) method consists of a multi-level strategy to approximate the solution of boundary value problems with heterogeneous coefficients. In this context, we propose a family of low-order finite elements for the…

Numerical Analysis · Mathematics 2024-03-26 Antônio Tadeu Azevedo Gomes , Weslley da Silva Pereira , Frédéric Valentin

A new family of mixed finite element methods$-$compatible-strain mixed finite element methods (CSFEMs)$-$are introduced for three-dimensional compressible and incompressible nonlinear elasticity. A Hu-Washizu-type functional is extremized…

Computational Engineering, Finance, and Science · Computer Science 2019-10-23 Mostafa Faghih Shojaei , Arash Yavari

A method is presented to calculate from first principles the higher-order elastic constants of a solid material. The method relies on finite strain deformations, a density functional theory approach to calculate the Cauchy stress tensor,…

Materials Science · Physics 2025-10-08 Ruvini Attanayake , Umesh C. Roy , Abhiyan Pandit , Angelo Bongiorno

We provide a detailed comparison of the two-dimensional, temporal and the spatiotemporal linearized analyses of the viscoelastic free shear flows in the limit of low to moderate Reynolds number and Elasticity number obeying four different…

Fluid Dynamics · Physics 2021-06-02 Diksha Bansal , Dipa Ghosh , Sarthok Sircar

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

In this work, a polygonal Reissner-Mindlin plate element is presented. The formulation is based on a scaled boundary finite element method, where in contrast to the original semi-analytical approach, linear shape functions are introduced…

Computational Engineering, Finance, and Science · Computer Science 2025-10-24 Anna Hellers , Mathias Reichle , Sven Klinkel

We consider a quadrilateral 'mini' finite element for approximating the solution of Stokes equations using a quadrilateral mesh. We use the standard bilinear finite element space enriched with element-wise defined bubble functions for the…

Numerical Analysis · Computer Science 2015-07-17 Bishnu P. Lamichhane

We formulate a cut finite element method for linear elasticity based on higher order elements on a fixed background mesh. Key to the method is a stabilization term which provides control of the jumps in the derivatives of the finite element…

Numerical Analysis · Mathematics 2019-02-05 Peter Hansbo , Mats G. Larson , Karl Larsson

We present a stable and convergent mixed finite element method (MFEM) for the linear regularized 13-moment (R13) equations in rarefied gas dynamics. Unlike existing methods that require stabilization via penalty terms, our scheme achieves…

Numerical Analysis · Mathematics 2026-01-27 Shuang Hu , Huiteng Li , Zhenning Cai

The paper addresses stability and finite element analysis of the stationary two-phase Stokes problem with a piecewise constant viscosity coefficient experiencing a jump across the interface between two fluid phases. We first prove a priori…

Numerical Analysis · Mathematics 2020-04-23 Ernesto Cáceres , Johnny Guzmán , Maxim Olshanskii

In this work we develop new finite element discretisations of the shear-deformable Reissner--Mindlin plate problem based on the Hellinger-Reissner principle of symmetric stresses. Specifically, we use conforming Hu-Zhang elements to…

Numerical Analysis · Mathematics 2023-05-30 Adam Sky , Michael Neunteufel , Jack S. Hale , Andreas Zilian

We introduce an arbitrary order, stabilized finite element method for solving a unique continuation problem subject to the time-harmonic elastic wave equation with variable coefficients. Based on conditional stability estimates we prove…

Numerical Analysis · Mathematics 2023-04-25 Erik Burman , Janosch Preuss

Within the framework of the displacement-based Virtual Element Method (VEM) for plane elasticity a significant problem is represented by an accurate evaluation of the stress field. In particular, in the classical VEM formulation, a suitable…

Numerical Analysis · Mathematics 2018-02-20 Edoardo Artioli , Stefano de Miranda , Carlo Lovadina , Luca Patruno

We consider mixed finite element methods with exact symmetric stress tensors. We derive a new quasi-optimal a priori error estimate uniformly valid with respect to the compressibility. For the a posteriori error analysis we consider the…

Numerical Analysis · Mathematics 2022-08-24 Philip L. Lederer , Rolf Stenberg

This article offers a new perspective for the mechanics of solids using moving Cartan's frame, specifically discussing a mixed variational principle in non-linear elasticity. We treat quantities defined on the co-tangent bundles of…

Computational Engineering, Finance, and Science · Computer Science 2022-04-06 Bensingh Dhas , Jamun Kumar N , Debasish Roy , J N Reddy

We present a stabilized, structure-preserving finite element framework for solving the Vlasov-Maxwell equations. The method uses a tensor product of continuous polynomial spaces for the spatial and velocity domains, respectively, to…

Numerical Analysis · Mathematics 2025-11-17 Katharina Kormann , Murtazo Nazarov , Junjie Wen