Abstrakt
The subject of the presented paper is a mathematical analysis and numerical solution of the system of nonlinear nonstationary reaction-diffusion equations. Firstly, using the invariant region technique, the proof of both the existence and uniqueness of the solution and problem data continuous dependence is carried out.
After time discretization of the problem the Galerkin finite elements method is applied and a priori error estimates of the method are derived. A suitable mesh adaptivity is discussed as well.
The method is finally implemented and tested on several examples.