An a posteriori error estimator for an unsteady advection-diffusion-reaction problem

In this work we introduce an a posteriori error estimator, of the residual type, for the unsteady advection-diffusion-reaction problem. For the discretization in time we use an implicit Euler scheme and a continuous, piecewise linear triangular finite elements for the space together with a stabilized scheme. We prove that the approximation error is bounded, by above and below, by the error estimator. Using that, an adaptive algorithm is proposed, analyzed and tested numerically to prove the efficiency of our approach. (C) 2013 Elsevier Ltd. All rights reserved.