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 article, a two-grid mixed finite element (TGMFE) method with somesecond-order time discrete schemes is developed for numerically solvingnonlinear fourth-order reaction diffusion equation. The two-grid MFE method isused to approximate spatial direction, and some second-order $\theta$ schemesformulated at time $t_{k-\theta}$ are considered to discretize the timedirection. TGMFE method covers two main steps: a nonlinear MFE system based onthe space coarse grid is solved by the iterative algorithm and a coarsesolution is arrived at, then a linearized MFE system with fine grid isconsidered and a TGMFE solution is obtained. Here, the stability and a priorierror estimates in $L^2$-norm for both nonlinear Galerkin MFE system and TGMFEscheme are derived. Finally, some convergence results are computed for bothnonlinear Galerkin MFE system and TGMFE scheme to verify our theoreticalanalysis, which show that the convergence rate of the time second-order$\theta$ scheme including Crank-Nicolson scheme and second-order backwarddifference scheme is close to $2$, and that with the comparison to thecomputing time of nonlinear Galerkin MFE method, the CPU-time by using TGMFEmethod can be saved.

TGMFE Algorithm Combined with Some Time Second-Order Schemes for Nonlinear Fourth-Order Reaction Diffusion System