Positivity-preserving and asymptotic preserving method for 2D Keller-Segal equations

Journal Article (Journal Article)

We propose a semi-discrete scheme for 2D Keller-Segel equations based on a symmetrization reformation, which is equivalent to the convex splitting method and is free of any nonlinear solver. We show that, this new scheme is stable as long as the initial condition does not exceed certain threshold, and it asymptotically preserves the quasi-static limit in the transient regime. Furthermore, we show that the fully discrete scheme is conservative and positivity preserving, which makes it ideal for simulations. The analogical schemes for the radial symmetric cases and the subcritical degenerate cases are also presented and analyzed. With extensive numerical tests, we verify the claimed properties of the methods and demonstrate their superiority in various challenging applications.

Full Text

Duke Authors

Cited Authors

  • Liu, JG; Wang, L; Zhou, Z

Published Date

  • January 1, 2018

Published In

Volume / Issue

  • 87 / 311

Start / End Page

  • 1165 - 1189

International Standard Serial Number (ISSN)

  • 0025-5718

Digital Object Identifier (DOI)

  • 10.1090/mcom/3250

Citation Source

  • Scopus