Fully discrete approximation by Galerkin Runge-Kutta methods for quasilinear parabolic systems
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.
scientific article; zbMATH DE number 1809818