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

This series of papers is devoted to the formulation and the approximation ofcoupling problems for nonlinear hyperbolic equations. The coupling across aninterface in the physical space is formulated in term of an augmented system ofpartial differential equations. In an earlier work, this strategy allowed us todevelop a regularization method based on a thick interface model in one spacevariable. In the present paper, we significantly extend this framework and, inaddition, encompass equations in several space variables. This new formulationincludes the coupling of several distinct conservation laws and allows for apossible covering in space. Our main contributions are, on one hand, the designand analysis of a well-balanced finite volume method on general triangulationsand, on the other hand, a proof of convergence of this method toward entropysolutions, extending Coquel, Cockburn, and LeFloch's theory (restricted to asingle conservation law without coupling). The core of our analysis is, first,the derivation of entropy inequalities as well as a discrete entropydissipation estimate and, second, a proof of convergence toward the entropysolution of the coupling problem.

Coupling techniques for nonlinear hyperbolic equations. IV. Multi-component coupling and multidimensional well-balanced schemes