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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

This paper focuses on the analysis of a free energy functional, that models a dilute suspension of magnetic nanoparticles in a two-dimensional nematic well. The {\it first part} of the article is devoted to the asymptotic analysis of global…

Numerical Analysis · Mathematics 2021-06-24 Ruma Rani Maity , Apala Majumdar , Neela Nataraj

The paper addresses the homogenization of a micro-model of poroelasticity coupled with thermal effects for two-constituent media and with imperfect interfacial contact.The homogenized model is obtained by means of the two-scale convergence…

Analysis of PDEs · Mathematics 2021-12-07 Abdelhamid Ainouz

We consider variational problems that model the bending behavior of curves that are constrained to belong to given hypersurfaces. Finite element discretizations of corresponding functionals are justified rigorously via Gamma-convergence.…

Numerical Analysis · Mathematics 2020-04-24 Sören Bartels

In this paper, we construct new finite element methods for the approximation of the equations of linear elasticity in three space dimensions that produce direct approximations to both stresses and displacements. The methods are based on a…

Numerical Analysis · Mathematics 2014-01-29 Douglas N. Arnold , Richard S. Falk , Ragnar Winther

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,…

Numerical Analysis · Mathematics 2018-02-09 Tobin Isaac

The aim of this paper is to develop a virtual element method (VEM) for the vibration problem of thin plates on polygonal meshes. We consider a variational formulation relying only on the transverse displacement of the plate and propose an…

Numerical Analysis · Mathematics 2017-03-14 David Mora , Gonzalo Rivera , Iván Velásquez

A reduced model for large deformations of prestrained plates consists of minimizing a second order bending energy subject to a nonconvex metric constraint. The former involves the second fundamental form of the middle plate and the later is…

Numerical Analysis · Mathematics 2020-11-03 Andrea Bonito , Diane Guignard , Ricardo H. Nochetto , Shuo Yang

This work is devoted to the development and analysis of a linearization algorithm for microscopic elliptic equations, with scaled degenerate production, posed in a perforated medium and constrained by the homogeneous Neumann-Dirichlet…

Numerical Analysis · Mathematics 2020-08-11 Anh-Khoa Vo , Ekeoma Rowland Ijioma , Nhu-Ngoc Nguyen

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…

Computational Engineering, Finance, and Science · Computer Science 2026-03-31 Sérgio G. F. Cordeiro , Boyang Chen , Frans P. van der Meer

We propose a parametric finite element method (PFEM) for efficiently solving the morphological evolution of solid-state dewetting of thin films on a flat rigid substrate in three dimensions (3D). The interface evolution of the dewetting…

Computational Physics · Physics 2020-03-03 Quan Zhao , Wei Jiang , Weizhu Bao

In this paper, we consider the numerical approximation for a diffuse interface model of the two-phase incompressible inductionless magnetohydrodynamics problem. This model consists of Cahn-Hilliard equations, Navier-Stokes equations and…

Numerical Analysis · Mathematics 2022-02-01 Xiaorong Wang , Xiaodi Zhang

We propose a generalized finite element method for linear elasticity equations with highly varying and oscillating coefficients. The method is formulated in the framework of localized orthogonal decomposition techniques introduced by…

Numerical Analysis · Mathematics 2016-08-24 Patrick Henning , Anna Persson

We study the discretisation of a uniaxial (rank-one) reduction of the Oldroyd-B model for dilute polymer solutions, in which the conformation tensor is represented as $\sig = \vec b \otimes \vec b$. Building on structural analogies with…

Numerical Analysis · Mathematics 2025-11-26 Ben S. Ashby , Gabriel R. Barrenechea , Alex Lukyanov , Tristan Pryer , Alex Trenam

Nematic elastomers and glasses deform spontaneously when subjected to temperature changes. This property can be exploited in the design of heterogeneously patterned thin sheets that deform into a non-trivial shape when heated or cooled. In…

Soft Condensed Matter · Physics 2017-10-25 Paul Plucinsky , Marius Lemm , Kaushik Bhattacharya

A novel general purpose Finite Element framework is presented to study small-scale metal plasticity. A distinct feature of the adopted distortion gradient plasticity formulation, with respect to strain gradient plasticity theories, is the…

Materials Science · Physics 2017-11-16 Emilio Martínez-Pañeda , Christian F. Niordson , Lorenzo Bardella

This work investigates finite element approximations for a general class of elliptic hemivariational inequalities arising in semipermeable media. The proposed model incorporates non-isotropic and heterogeneous diffusion coefficients,…

Numerical Analysis · Mathematics 2026-05-05 Ban Li , Bangmin Wu

We construct finite element subspaces of the space of symmetric tensors with square-integrable divergence on a three-dimensional domain. These spaces can be used to approximate the stress field in the classical Hellinger--Reissner mixed…

Numerical Analysis · Mathematics 2014-01-29 Douglas N. Arnold , Gerard Awanou , Ragnar Winther

This paper deals with the approximation and homogenization of thermoelastic wave model. First, we study the homogenization problem of a weakly coupled thermoelastic wave model with rapidly varying coefficients, using a semigroup approach,…

Analysis of PDEs · Mathematics 2023-06-29 Salem Nafiri

We derive a hierarchy of plate theories for heterogeneous multilayers from three dimensional nonlinear elasticity by means of $\Gamma$-convergence. We allow for layers composed of different materials whose constitutive assumptions may vary…

Analysis of PDEs · Mathematics 2019-05-28 Miguel de Benito Delgado , Bernd Schmidt