Fully Discrete Analysis of a Discontinuous Finite Element Method for the Keller-Segel Chemotaxis Model

被引：43
|
作者：
Epshteyn, Yekaterina [1 ]
Izmirlioglu, Ahmet [2 ]
机构：
[1] Carnegie Mellon Univ, Dept Math Sci, Pittsburgh, PA 15213 USA
[2] Univ Pittsburgh, Dept Math, Pittsburgh, PA 15260 USA
来源：
JOURNAL OF SCIENTIFIC COMPUTING | 2009年 / 40卷 / 1-3期
基金：
美国国家科学基金会;
关键词：
Keller-Segel chemotaxis model; Convection-diffusion-reaction systems; Discontinuous Galerkin methods; Forward Euler; Runge-Kutta; NIPG; IIPG; and SIPG methods; Cartesian meshes; CENTRAL-UPWIND SCHEMES; CONSERVATION-LAWS; GALERKIN METHODS; P-VERSION; AGGREGATION; BACTERIA; CONVERGENCE; EQUATIONS; PATTERNS; SYSTEMS;
D O I：
10.1007/s10915-009-9281-5
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
This paper formulates and analyzes fully discrete schemes for the two-dimensional Keller-Segel chemotaxis model. The spatial discretization of the model is based on the discontinuous Galerkin methods and the temporal discretization is based either on Forward Euler or the second order explicit total variation diminishing (TVD) Runge-Kutta methods. We consider Cartesian grids and prove fully discrete error estimates for the proposed methods. Our proof is valid for pre-blow-up times since we assume boundedness of the exact solution.
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页码：211 / 256
页数：46
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