Finite volume methods for a Keller-Segel system: discrete energy, error estimates and numerical blow-up analysis
type: Item
instance of: scholarly article
title: Finite volume methods for a Keller-Segel system: discrete energy, error estimates and numerical blow-up analysis
zbMATH Open document ID: 1360.65225
author: Guanyu Zhou
author: Norikazu Saito
published in: Numerische Mathematik
publication date: 2017-01-25T00:00:00Z
review text: The authors applies the finite volume method to approximately solve the parabolic-elliptic system of the form \[ \frac{\partial u}{\partial t}=\nabla(\nabla u- u\nabla v), \] \[ -\Delta v + v=u \text{ in }\Omega \times [0,T], \,\Omega \subset \mathbb R^{2}, \] with the initial condition \( u(x,0)=u_{0}(x)\) on \(\Omega \) and homogenous boundary conditions for the fist derivatives of \(u\) and\(v\) on \( \Gamma =\partial \Omega.\) To preserve the essential properties of the exact problem -- the conservation laws and free energy -- several conditions are imposed in the construction of the mesh and adequate approximate scheme. The error estimate and blow-up phenomenon for approximate solutions are shown by numerical results for two examples on the rectangular and circular domains.
Mathematics Subject Classification ID: 65M08
Mathematics Subject Classification ID: 65M15
Mathematics Subject Classification ID: 35M33
zbMATH DE Number: 6677840
zbMATH Keywords: nonlinear parabolic-elliptic system
zbMATH Keywords: finite volume method
zbMATH Keywords: error estimate
zbMATH Keywords: blow-up phenomenon
zbMATH Keywords: numerical result
describes a project that uses: Chemotaxis
reviewed by: Ivan Secrieru
MaRDI profile type: Publication
full work available at URL: s00211-016-0793-2
OpenAlex ID: W2345240758
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DOI: 10.1007/S00211-016-0793-2
description: scientific article; zbMATH DE number 6677840