English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Tools annual

Global: Zendy Free Plan

Global: Zendy Tools monthly

Global: Zendy Plus monthly

In this paper, we study a mixed discontinuous Galerkin (MDG) method to solve linear elasticity problem with arbitrary order discontinuous finite element spaces in $d$-dimension ($d=2,3$). This method uses polynomials of degree $k+1$ for the stress and of degree $k$ for the displacement ($k\geq 0$). The mixed DG scheme is proved to be well-posed under proper norms. Specifically, we prove that, for any $k \geq 0$, the $H({\rm div})$-like error estimate for the stress and $L^2$ error estimate for the displacement are optimal. We further establish the optimal $L^2$ error estimate for the stress provided that the $\mathcal{P}_{k+2}-\mathcal{P}_{k+1}^{-1}$ Stokes pair is stable and $k \geq d$. We also provide numerical results of MDG showing that the orders of convergence are actually sharp.

A Mixed Discontinuous Galerkin Method for Linear Elasticity with Strongly Imposed Symmetry