2017年1月
Finite volume methods for a Keller-Segel system: discrete energy, error estimates and numerical blow-up analysis
NUMERISCHE MATHEMATIK
- ,
- 巻
- 135
- 号
- 1
- 開始ページ
- 265
- 終了ページ
- 311
- 記述言語
- 英語
- 掲載種別
- 研究論文(学術雑誌)
- DOI
- 10.1007/s00211-016-0793-2
- 出版者・発行元
- SPRINGER HEIDELBERG
We consider the finite volume approximation for a non-linear parabolic-elliptic system, which describes the aggregation of slime molds resulting from their chemotactic features, called a simplified Keller-Segel system. First, we present a linear finite volume scheme that satisfies both positivity and mass conservations, which are important features of the original system. We derive some inequalities on the discrete free energy. Then, under some assumptions on the regularity of solution, admissible mesh and a priori estimates of the discrete solution, we establish error estimates in norm with a suitable for the two dimensional case. In the last part of this paper, we restrict our attention to the radially symmetric solution of chemotaxis system, and we derive some inequalities concerned with the blow-up phenomenon of numerical solution. Several numerical experiments are presented to verify the theoretical results.
- リンク情報
- ID情報
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- DOI : 10.1007/s00211-016-0793-2
- ISSN : 0029-599X
- eISSN : 0945-3245
- Web of Science ID : WOS:000392032600009