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 Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

We consider so-called Herrmann and Hydrostatic mixed formulations ofclassical linear elasticity and analyse the error associated with locallystabilised $P_1-P_0$ finite element approximation. First, we prove a stabilityestimate for the discrete problem and establish an a priori estimate for theassociated energy error. Second, we consider a residual-based a posteriorierror estimator as well as a local Poisson problem estimator. We establishbounds for the energy error that are independent of the Lam\'{e} coefficientsand prove that the estimators are robust in the incompressible limit. A keyissue to be addressed is the requirement for pressure stabilisation. Numericalresults are presented that validate the theory. The software used is availableonline.

Robust error estimation for lowest-order approximation of nearly incompressible elasticity