Adaptive finite element methods for systems of reaction-diffusion equations Original Research Article

We consider an adaptive finite element method with quantitative error control for systems of reaction-diffusion equations. The adaptive algorithm is based on an a posteriori error estimate involving residuals of the computed solution and certain strong stability factors, which are estimated by solving an associated linearized dual problem numerically. To take into account that the stability properties in space and time are different, separate stability factors are used for the space discretization and the time discretization.