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

We present a paradigm for developing arbitrarily high order, linear,unconditionally energy stable numerical algorithms for gradient flow models. Weapply the energy quadratization (EQ) technique to reformulate the generalgradient flow model into an equivalent gradient flow model with a quadraticfree energy and a modified mobility. Given solutions up to $t_n=n \Delta t$with $\Delta t$ the time step size, we linearize the EQ-reformulated gradientflow model in $(t_n, t_{n+1}]$ by extrapolation. Then we employ analgebraically stable Runge-Kutta method to discretize the linearized model in$(t_n, t_{n+1}]$. Then we use the Fourier pseudo-spectral method for thespatial discretization to match the order of accuracy in time. The resultingfully discrete scheme is linear, unconditionally energy stable, uniquelysolvable, and may reach arbitrarily high order. Furthermore, we present afamily of linear schemes based on prediction-correction methods to complementthe new linear schemes. Some benchmark numerical examples are given todemonstrate the accuracy and efficiency of the schemes.

Arbitrarily High-order Linear Schemes for Gradient Flow Models