Fully discrete approximation by Galerkin Runge-Kutta methods for quasilinear parabolic systems
type: Item
instance of: scholarly article
title: Fully discrete approximation by Galerkin Runge-Kutta methods for quasilinear parabolic systems
zbMATH Open document ID: 1011.65067
author: Etsushi Nakaguchi
author: Atsushi Yagi
published in: Hokkaido Mathematical Journal
publication date: 2003-05-14T00:00:00Z
review text: A mathematical model describing aggregating patterns induced by the effects of chemotaxis and growth is presented. From the mathematical point of view this model is a quasilinear diffusion parabolic system with homogeneous Neumann boundary condition in a 2D region, and the unknown functions represent the population density of biological individuals and the concentration of chemical substance. A fully discretization scheme based on Galerkin and Runge-Kutta methods, employing semigroups of linear operators is investigated. Stability in \(L_2(\Omega)\) norm and an error estimate in \( H^{1+\varepsilon}( \Omega), \;\varepsilon >0\), are established. The conclusion of this paper is devoted to abstract quasilinear evolution equations in order to fix the numerical method presented before in a general form.
reviewed by: Angela Handlovičová
Mathematics Subject Classification ID: 65M60
Mathematics Subject Classification ID: 65M12
Mathematics Subject Classification ID: 35K90
Mathematics Subject Classification ID: 65J15
Mathematics Subject Classification ID: 65M15
Mathematics Subject Classification ID: 65L06
Mathematics Subject Classification ID: 35K55
zbMATH DE Number: 1809818
zbMATH Keywords: quasilinear parabolic systems
zbMATH Keywords: implicit Runge-Kutta methods
zbMATH Keywords: Galerkin finite element method
zbMATH Keywords: stability
zbMATH Keywords: error estimates
zbMATH Keywords: population dynamics
zbMATH Keywords: chemotaxis
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.14492/hokmj/1350911871
OpenAlex ID: W2049984506
DOI: 10.14492/HOKMJ/1350911871
description: scientific article; zbMATH DE number 1809818