Convergence in the incompressible limit of new discontinuous Galerkin methods with general quadrilateral and hexahedral elements

by   Beverley J. Grieshaber, et al.

Standard low-order finite elements, which perform well for problems involving compressible elastic materials, are known to under-perform when nearly incompressible materials are involved, commonly exhibiting the locking phenomenon. Interior penalty (IP) discontinuous Galerkin methods have been shown to circumvent locking when simplicial elements are used. The same IP methods, however, result in locking on meshes of quadrilaterals. The authors have shown in earlier work that under-integration of specified terms in the IP formulation eliminates the locking problem for rectangular elements. Here it is demonstrated through an extensive numerical investigation that the effect of using under-integration carries over successfully to meshes of more general quadrilateral elements, as would likely be used in practical applications, and results in accurate displacement approximations. Uniform convergence with respect to the compressibility parameter is shown numerically. Additionally, a stress approximation obtained here by postprocessing shows good convergence in the incompressible limit.



There are no comments yet.


page 14

page 21

page 22

page 23

page 29

page 30

page 32

page 37


A robust discontinuous Galerkin scheme on anisotropic meshes

Discontinuous Galerkin (DG) methods are extensions of the usual Galerkin...

A short note on the accuracy of the discontinuous Galerkin method with reentrant faces

We study the convergence of the discontinuous Galerkin (DG) method appli...

Stability and Convergence of Spectral Mixed Discontinuous Galerkin Methods for 3D Linear Elasticity on Anisotropic Geometric Meshes

We consider spectral mixed discontinuous Galerkin finite element discret...

Sub-optimal convergence of discontinuous Galerkin methods with central fluxes for even degree polynomial approximations

In this paper, we theoretically and numerically verify that the disconti...

GPU-accelerated discontinuous Galerkin methods on polytopic meshes

Discontinuous Galerkin (dG) methods on meshes consisting of polygonal/po...

On some nonlocal models with radially symmetric interaction domains and the effect of domain truncation

Many nonlocal models have adopted a finite and radially symmetric nonloc...
This week in AI

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