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/

Zendy Pro

Presents the zaia usage as premium feature

ZAIA

Presents AI Discovery search usage as a premium feature

AI Discovery

Presents AI Discovery explain and summary usage as a premium feature

Content Analysis

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Presents the pdf analysis as premium feature

PDF Analysis

1500 Top-up

3000 Top-up

Zendy Basic

2500 Top-up

Zendy Unlimited

Presents the access of premium content as premium feature

Premium Content

This paper is the third of a series in which a general theory of a priori error estimates for scalar conservation laws is constructed. In this paper, we consider multidimensional flux-splitting monotone schemes defined on non-Cartesian grids. We identify those schemes which are consistent and prove that the $L^\infty(0,T;L^1(\Bbb{R}^d))$-norm of the error goes to zero as $(\Delta x)^{1/2}$ when the discretization parameter $\Delta x$ goes to zero. Moreover, we show that nonconsistent schemes can converge at optimal rates of $(\Delta x)^{1/2}$ because (i) the conservation form of the schemes and (ii) the so-called consistency of the numerical fluxes allow the regularity properties of the approximate solution to compensate for their lack of consistency.

siam journal on numerical analysis

A Priori Error Estimates for Numerical Methods for Scalar Conservation Laws Part III: Multidimensional Flux-Splitting Monotone Schemes on Non-Cartesian Grids