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

Due to their algorithmic simplicity and high accuracy, force-based modelcoupling techniques are an exciting development in computational physics. Forexample, the force-based quasicontinuum approximation is the only knownpointwise consistent quasicontinuum approximation for coupling a generalatomistic model with a finite element continuum model. In this paper, weanalyze the stability of the force-based quasicontinuum approximation. We thenuse our stability result to obtain an optimal order error analysis of thiscoupling method that provides theoretical justification for the high accuracyof the force-based quasicontinuum approximation -- the computational efficiencyof continuum modeling can be utilized without the loss of significant accuracyif defects are captured in the atomistic region. The main challenge we need toovercome is the fact (which we prove) that the linearized quasicontinuumoperator is typically not positive definite. Moreover, we prove that no uniforminf-sup stability condition holds for discrete versions of the$W^{1,p}$-$W^{1,q}$ "duality pairing" with $1/p+1/q=1$, if $1 \leq p < \infty$.We must therefore derive an inf-sup stability condition for a discrete versionof the $W^{1,\infty}$-$W^{1,1}$ "duality pairing" which then leads to optimalorder error estimates in a discrete $W^{1,\infty}$-norm.

Stability, Instability, and Error of the Force-based Quasicontinuum Approximation