Error estimates for discrete-time approximations of nonlinear cross-diffusion systems

Hideki Murakawa

Research output: Contribution to journalArticle

5 Citations (Scopus)

Abstract

This paper is concerned with nonlinear and linear discrete-time algorithms for crossdiffusion systems. The nonlinear scheme corresponds to backward differences in time, and the linear algorithm is a very-easy-to-implement scheme proposed by the author [ESAIMMath. Model. Numer. Anal., 45 (2011), pp. 1141-1161]. The main purpose of this paper is to derive convergence rates of the discrete-time schemes. We obtain the same orders for both the nonlinear and the linear scheme. Moreover, these orders are optimal. We also establish uniqueness and regularity results of weak solutions of the cross-diffusion systems.

Original languageEnglish
Pages (from-to)955-974
Number of pages20
JournalSIAM Journal on Numerical Analysis
Volume52
Issue number2
DOIs
Publication statusPublished - 2014

All Science Journal Classification (ASJC) codes

  • Numerical Analysis
  • Computational Mathematics
  • Applied Mathematics

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