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, a linear second order numerical scheme is developed andinvestigated for the Allen-Cahn equation with a general positive mobility. Inparticular, our fully discrete scheme is mainly constructed based on theCrank-Nicolson formula for temporal discretization and the central finitedifference method for spatial approximation, and two extra stabilizing termsare also introduced for the purpose of improving numerical stability. Theproposed scheme is shown to unconditionally preserve the maximum boundprinciple (MBP) under mild restrictions on the stabilization parameters, whichis of practical importance for achieving good accuracy and stabilitysimultaneously. With the help of uniform boundedness of the numerical solutionsdue to MBP, we then successfully derive $H^{1}$-norm and $L^{\infty}$-normerror estimates for the Allen-Cahn equation with a constant and a variablemobility, respectively. Moreover, the energy stability of the proposed schemeis also obtained in the sense that the discrete free energy is uniformlybounded by the one at the initial time plus a {\color{black}constant}. Finally,some numerical experiments are carried out to verify the theoretical resultsand illustrate the performance of the proposed scheme with a time adaptivestrategy.

A linear doubly stabilized Crank-Nicolson scheme for the Allen-Cahn equation with a general mobility