Robust a-posteriori estimators for multilevel discretizations of reaction-diffusion systems
V. Klein 1, M. Peszynska 11 Department of Mathematics, Oregon State University, Corvallis, OR 97331, USA.
Received by the editors March 2, 2010 and, in revised form, April 21, 2010.
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.AMS subject classifications: 65N30, 65N15
Key words: multilevel finite elements, a-priori error estimates, a-posteriori error estimators, reaction-diffusion system.
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