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

For discretisations of hyperbolic conservation laws, mimicking properties ofoperators or solutions at the continuous (differential equation) leveldiscretely has resulted in several successful methods. While well-posedness fornonlinear systems in several space dimensions is an open problem, mimeticproperties such as summation-by-parts as discrete analogue ofintegration-by-parts allow a direct transfer of some results and their proofs,e.g. stability for linear systems.  In this article, discrete analogues of the generalised product and chainrules that apply to functions of bounded variation are considered. It is shownthat such analogues hold for certain second order operators but are notpossible for higher order approximations. Furthermore, entropy dissipation bysecond derivatives with varying coefficients is investigated, showing again thefar stronger mimetic properties of second order approximations compared tohigher order ones.

bit/bit numerical mathematics

Mimetic Properties of Difference Operators: Product and Chain Rules as  for Functions of Bounded Variation and Entropy Stability of Second  Derivatives