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

The existing discrete variational derivative method is only second-orderaccurate and fully implicit. In this paper, we propose a framework to constructan arbitrary high-order implicit (original) energy stable scheme and asecond-order semi-implicit (modified) energy stable scheme. Combined with theRunge--Kutta process, we can build an arbitrary high-order and unconditionally(original) energy stable scheme based on the discrete variational derivativemethod. The new energy stable scheme is implicit and leads to a large sparsenonlinear algebraic system at each time step, which can be efficiently solvedby using an inexact Newton type algorithm. To avoid solving nonlinear algebraicsystems, we then present a relaxed discrete variational derivative method,which can construct second-order, linear, and unconditionally (modified) energystable schemes. Several numerical simulations are performed to investigate theefficiency, stability, and accuracy of the newly proposed schemes.

Energy stable schemes for gradient flows based on the DVD method