An Unconditionally Energy Stable and Positive Upwind DG Scheme for the Keller-Segel Model

被引：8

作者：

Acosta-Soba, Daniel ^{[1
,2
]}

Guillen-Gonzalez, Francisco ^{[3
,4
]}

Rodriguez-Galvan, J. Rafael ^{[1
]}

机构：

[1] Univ Cadiz, Dept Matemat, Puerto Real, Spain

[2] Univ Tennessee Chattanooga, Dept Math, Chattanooga, TN USA

[3] Univ Seville, Dept Ecuaciones Diferenci & Anal Numer, Seville, Spain

[4] Univ Seville, IMUS, Seville, Spain

来源：

JOURNAL OF SCIENTIFIC COMPUTING | 2023年 / 97卷 / 01期

关键词：

Keller-Segel equations; Chemotaxis; Discontinuous Galerkin; Upwind scheme; Positivity preserving; Energy stability; DISCONTINUOUS GALERKIN METHODS; FINITE-ELEMENT-METHOD; BLOW-UP; CHEMOTAXIS; SYSTEM; APPROXIMATION;

D O I：

10.1007/s10915-023-02320-4

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

The well-suited discretization of the Keller-Segel equations for chemotaxis has become a very challenging problem due to the convective nature inherent to them. This paper aims to introduce a new upwind, mass-conservative, positive and energy-dissipative discontinuous Galerkin scheme for the Keller-Segel model. This approach is based on the gradient-flow structure of the equations. In addition, we show some numerical experiments in accordance with the aforementioned properties of the discretization. The numerical results obtained emphasize the really good behaviour of the approximation in the case of chemotactic collapse, where very steep gradients appear.

引用

页数：27

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