Time--Splitting Schemes and Measure Source Terms for a Quasilinear Relaxing System

TL;DR

This paper investigates singular limits of a 2x2 system modeling chromatographic processes, focusing on time-splitting schemes and measure source terms with Dirac measures to facilitate numerical analysis.

Contribution

It introduces a novel approach using Dirac measures to analyze time-splitting schemes for a quasilinear relaxing system, enhancing understanding of singular limits in this context.

Findings

Analysis of singular limits in the system

Development of time-splitting numerical schemes

Use of Dirac measures for measure source terms

Abstract

Several singular limits are investigated in the context of a $2 \times 2$ system arising for instance in the modeling of chromatographic processes. In particular, we focus on the case where the relaxation term and a $L^2$ projection operator are concentrated on a discrete lattice by means of Dirac measures. This formulation allows to study more easily some time-splitting numerical schemes.