A family of mixed finite elements for nearly incompressible strain gradient elastic models

05/01/2021
by   Yulei Liao, et al.
0

We propose a family of mixed finite elements that are robust for the nearly incompressible strain gradient model. A discrete B-B inequality is proved for the mixed finite element approximation, which is uniform with respect to the microscopic parameter. Optimal rate of convergence is proved that is robust in the incompressible limit. Numerical results confirm the theoretical prediction.

READ FULL TEXT
POST COMMENT

Comments

There are no comments yet.

Authors

page 1

page 2

page 3

page 4

09/05/2019

Quasi-optimal adaptive hybridized mixed finite element methods for linear elasticity

For the planar elasticity equation, we prove the uniform convergence and...
04/17/2021

H^2- Korn's Inequality and the Nonconforming Elements for The Strain Gradient Elastic Model

We establish a new H2 Korn's inequality and its discrete analog, which g...
09/18/2019

3D H^2-nonconforming tetrahedral finite elements for the biharmonic equation

In this article, a family of H^2-nonconforming finite elements on tetrah...
03/03/2020

Preconditioning mixed finite elements for tide models

We describe a fully discrete mixed finite element method for the lineari...
10/31/2021

An accurate, robust, and efficient finite element framework for anisotropic, nearly and fully incompressible elasticity

Fiber-reinforced soft biological tissues are typically modeled as hypere...
01/24/2020

Generalized Prager-Synge Inequality and Equilibrated Error Estimators for Discontinuous Elements

The well-known Prager-Synge identity is valid in H^1(Ω) and serves as a ...
04/29/2022

Node-based uniform strain virtual elements for compressible and nearly incompressible plane elasticity

We propose a combined nodal integration and virtual element method for c...
This week in AI

Get the week's most popular data science and artificial intelligence research sent straight to your inbox every Saturday.