Robust a-Posteriori Estimators for Multilevel Discretizations of Reaction-Diffusion Systems
Keywords:
multilevel finite elements, a-priori error estimates, a-posteriori error estimators, reaction-diffusion system.Abstract
We define a multilevel finite element discretization for a coupled stationary reaction-diffusion system in which each component can be defined on a separate grid. We prove convergence of the scheme and propose residual a-posteriori estimators for the error in the natural energy norm for the system. The estimators are robust in the coefficients of the system. We prove upper and lower bounds and illustrate the theory with numerical experiments.