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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

In this paper, we propose a robust solver for the finite element discrete problem of the stationary incompressible magnetohydrodynamic (MHD) equations in three dimensions. By the mixed finite element method, both the velocity and the…

Numerical Analysis · Mathematics 2017-10-23 Lingxiao Li , Weiying Zheng

We consider a mixed finite element method for approximating the solution of nearly incompressible elasticity and Stokes equations. The finite element method is based on quadrilateral and hexahedral triangulation using primal and dual…

Numerical Analysis · Mathematics 2013-10-23 Bishnu P. Lamichhane

We construct a finite element approximation of a strain-limiting elastic model on a bounded open domain in $\mathbb{R}^d$, $d \in \{2,3\}$. The sequence of finite element approximations is shown to exhibit strong convergence to the unique…

Numerical Analysis · Mathematics 2020-04-02 Andrea Bonito , Vivette Girault , Endre Süli

We study a finite element approximation of a coupled fluid-structure interaction consisting of a three-dimensional incompressible viscous fluid governed by the unsteady Stokes equations and a two-dimensional elastic plate. To avoid the use…

Numerical Analysis · Mathematics 2026-02-10 Lander Besabe , Hyesuk Lee

In this paper we study finite element method for three-dimensional incompressible resistive magnetohydrodynamic equations, in which the velocity, the current density, and the magnetic induction are divergence-free. It is desirable that the…

Numerical Analysis · Mathematics 2021-02-03 Lingxiao Li , Donghang Zhang , Weiying Zheng

The thin plate spline is a popular tool for the interpolation and smoothing of scattered data. In this paper we propose a novel stabilized mixed finite element method for the discretization of thin plate splines. The mixed formulation is…

Numerical Analysis · Mathematics 2013-05-13 Bishnu P. Lamichhane , Markus Hegland

We present a finite element discretisation to model the interaction between a poroelastic structure and an elastic medium. The consolidation problem considers fully coupled deformations across an interface, ensuring continuity of…

Numerical Analysis · Mathematics 2023-06-21 S. Badia , M. Hornkjøl , A. Khan , K. -A. Mardal , A. F. Martín , R. Ruiz-Baier

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…

Numerical Analysis · Mathematics 2026-01-30 Giovanni Taraschi , Maicon Ribeiro Correa

A new high-order conservative finite element method for Darcy flow is presented. The key ingredient in the formulation is a volumetric, residual-based, based on Lagrange multipliers in order to impose conservation of mass that does not…

Numerical Analysis · Mathematics 2017-07-03 Eduardo Abreu , Ciro Diaz , Juan Galvis , Marcus Sarkis

We propose an enriched finite element formulation to address the computational modeling of contact problems and the coupling of non-conforming discretizations in the small deformation setting. The displacement field is augmented by enriched…

Computational Engineering, Finance, and Science · Computer Science 2021-12-30 Dongyu Liu , Sanne J. van den Boom , Angelo Simone , Alejandro M. Aragón

This paper presents a family of mixed finite elements on triangular grids for solving the classical Hellinger-Reissner mixed problem of the elasticity equations. In these elements, the matrix-valued stress field is approximated by the full…

Numerical Analysis · Mathematics 2015-01-22 Jun Hu , Shangyou Zhang

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

We propose two parameter-robust mixed finite element methods for linear Cosserat elasticity. The Cosserat coupling constant $\mu_c$, connecting the displacement $u$ and rotation vector $\omega$, leads to possible locking phenomena in finite…

Numerical Analysis · Mathematics 2025-09-19 Andrea Dziubek , Kaibo Hu , Michael Karow , Michael Neunteufel

A novel mixed-hybrid method for Kirchhoff-Love shells is proposed that enables the use of classical, possibly higher-order Lagrange elements in numerical analyses. In contrast to purely displacement-based formulations that require higher…

Computational Engineering, Finance, and Science · Computer Science 2026-02-17 Jonas Neumeyer , Michael Wolfgang Kaiser , Thomas-Peter Fries

In this paper we address three aspects of nonlinear computational homogenization of elastic solids by two-scale finite element methods. First, we present a nonlinear formulation of the finite element heterogeneous multiscale method FE-HMM…

Numerical Analysis · Mathematics 2019-12-24 Bernhard Eidel , Andreas Fischer , Ajinkya Gote

In this paper, we propose a parallel solver for solving the quasi-static linear poroelasticity coupled with linear elasticity model in the Lagrange multiplier framework. Firstly, we reformulate the model into a coupling of the nearly…

Numerical Analysis · Mathematics 2025-09-09 Zhihao Ge , Chengxin Wang

We propose two classes of mixed finite elements for linear elasticity of any order, with interior penalty for nonconforming symmetric stress approximation. One key point of our method is to introduce some appropriate nonconforming…

Numerical Analysis · Mathematics 2017-05-22 Shuonan Wu , Shihua Gong , Jinchao Xu

The fourth-order PDE that models the density variation of smectic A liquid crystals presents unique challenges in its (numerical) analysis beyond more common fourth-order operators, such as the classical biharmonic. While the operator is…

Numerical Analysis · Mathematics 2023-08-24 Patrick E. Farrell , Abdalaziz Hamdan , Scott P. MacLachlan

We introduce a new formulation for the finite element immersed boundary method which makes use of a distributed Lagrange multiplier. We prove that a full discretization of our model, based on a semi-implicit time advancing scheme, is…

Numerical Analysis · Mathematics 2015-03-05 Daniele Boffi , Nicola Cavallini , Lucia Gastaldi