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

In this paper, we consider a novel auxiliary variable method to obtain energystable schemes for gradient flows. The auxiliary variable based on energybounded above does not limited to the hypothetical conditions adopted inprevious approaches. We proved the unconditional energy stability for all thesemi-discrete schemes carefully and rigorously. The novelty of the proposedschemes is that the computed values for the functional in square root areguaranteed to be positive. This method, termed novel auxiliary energy variable(NAEV) method does not consider any bounded below restrictions any longer.However, these restrictions are necessary in invariant energy quadratization(IEQ) and scalar auxiliary variable (SAV) approaches which are very popularmethods recently. This property of guaranteed positivity is not available inprevious approaches. A comparative study of classical SAV and NAEV approachesis considered to show the accuracy and efficiency. Finally, we present various2D numerical simulations to demonstrate the stability and accuracy.

Energy stable schemes for gradient flows based on novel auxiliary variable with energy bounded above