English
Related papers

Related papers: A locking free multiscale method for linear elasti…

200 papers

In this work we construct a low-order nonconforming approximation method for linear elasticity problems supporting general meshes and valid in two and three space dimensions. The method is obtained by hacking the Hybrid High-Order method,…

Numerical Analysis · Mathematics 2019-06-26 Michele Botti , Daniele A. Di Pietro , Alessandra Guglielmana

A block diagonal preconditioner with the minimal residual method and a block triangular preconditioner with the generalized minimal residual method are developed for Hu-Zhang mixed finite element methods of linear elasticity. They are based…

Numerical Analysis · Mathematics 2016-05-24 Long Chen , Jun Hu , Xuehai Huang

The dual formulation for linear elasticity, in contrast to the primal formulation, is not affected by locking, as it is based on the stresses as main unknowns. Thus it is quite attractive for nearly incompressible and incompressible…

Numerical Analysis · Mathematics 2021-06-28 Gabriele Rovi , Rolf Krause

The purpose of this work is to study mortar methods for linear elasticity using standard low order finite element spaces. Based on residual stabilization, we introduce a stabilized mortar method for linear elasticity and compare it to the…

Numerical Analysis · Mathematics 2022-12-28 Tom Gustafsson , Peter Råback , Juha Videman

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…

Mathematical Physics · Physics 2014-03-17 Patrizio Neff , Ionel-Dumitrel Ghiba , Markus Lazar , Angela Madeo

We introduce a new discretization of a mixed formulation of the incompressible Stokes equations that includes symmetric viscous stresses. The method is built upon a mass conserving mixed formulation that we recently studied. The improvement…

Numerical Analysis · Mathematics 2024-12-20 Jay Gopalakrishnan , Philip L. Lederer , Joachim Schöberl

This paper proposes a methodology to estimate stress in the subsurface by a hybrid method combining finite element modeling and neural networks. This methodology exploits the idea of obtaining a multi-frequency solution in the numerical…

Machine Learning · Computer Science 2020-08-27 Xavier Garcia , Adrian Rodriguez-Herrera

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…

Numerical Analysis · Mathematics 2025-03-17 Carsten Carstensen , Norbert Heuer

We introduce a new cell-centered finite volume discretization for elasticity with weakly enforced symmetry of the stress tensor. The method is motivated by the need for robust discretization methods for deformation and flow in porous media,…

Numerical Analysis · Mathematics 2015-12-04 Eirik Keilegavlen , Jan Martin Nordbotten

This paper presents a new hybridizable discontinuous Galerkin (HDG) method for linear elasticity on general polyhedral meshes, based on a strong symmetric stress formulation. The key feature of this new HDG method is the use of a special…

Numerical Analysis · Mathematics 2016-02-24 Weifeng Qiu , Jiguang Shen , Ke Shi

We develop a mixed finite element domain decomposition method on non-matching grids for the Biot system of poroelasticity. A displacement-pressure vector mortar function is introduced on the interfaces and utilized as a Lagrange multiplier…

Numerical Analysis · Mathematics 2024-09-13 Manu Jayadharan , Ivan Yotov

We present an ``equation-free'' multiscale approach to the simulation of unsteady diffusion in a random medium. The diffusivity of the medium is modeled as a random field with short correlation length, and the governing equations are cast…

Numerical Analysis · Mathematics 2007-05-23 Dongbin Xiu , Ioannis Kevrekidis

This work presents a matrix-free finite element solver for finite-strain elasticity adopting an $hp$-multigrid preconditioner. Compared to classical algorithms relying on a global sparse matrix, matrix-free solution strategies significantly…

Computational Engineering, Finance, and Science · Computer Science 2024-12-09 Richard Schussnig , Niklas Fehn , Peter Munch , Martin Kronbichler

We present a stable finite element method for incompressible nonlinear elasticity based on a four-field mixed formulation involving the displacement, displacement gradient, first Piola--Kirchhoff stress and pressure. Unlike existing…

Numerical Analysis · Mathematics 2026-03-11 Santiago Badia , Wei Li , Ricardo Ruiz-Baier

We introduce and analyze a stress-based formulation for Zener's model in linear viscoelasticity. The method is aimed to tackle efficiently heterogeneous materials that admit purely elastic and viscoelastic parts in their composition. We…

Numerical Analysis · Mathematics 2020-10-19 Antonio Márquez , Salim Meddahi

We develop a new multipoint stress mixed finite element method for linear elasticity with weakly enforced stress symmetry on simplicial grids. Motivated by the multipoint flux mixed finite element method for Darcy flow, the method utilizes…

Numerical Analysis · Mathematics 2019-07-30 Ilona Ambartsumyan , Eldar Khattatov , Jan M. Nordbotten , Ivan Yotov

This paper presents a new and unified approach to the derivation and analysis of many existing, as well as new discontinuous Galerkin methods for linear elasticity problems. The analysis is based on a unified discrete formulation for the…

Numerical Analysis · Mathematics 2021-10-12 Qingguo Hong , Jun Hu , Limin Ma , Jinchao Xu

In this work, we generalize the mass-conserving mixed stress (MCS) finite element method for Stokes equations [Gopalakrishnan J., Lederer P., and Sch\"oberl J., A mass conserving mixed stress formulation for the Stokes equations, IMA…

Numerical Analysis · Mathematics 2025-09-19 Guosheng Fu , Michael Neunteufel , Joachim Schöberl , Adam Zdunek

An isogeometric boundary element method for problems in elasticity is presented, which is based on an independent approximation for the geometry, traction and displacement field. This enables a flexible choice of refinement strategies,…

Numerical Analysis · Computer Science 2015-02-04 Benjamin Marussig , Jürgen Zechner , Gernot Beer , Thomas-Peter Fries

An efficient and reliable stress computation algorithm is presented, which is based on implicit integration of the local evolution equations of multiplicative finite-strain plasticity/viscoplasticity. The algorithm is illustrated by an…

Numerical Analysis · Mathematics 2016-05-25 A. V. Shutov