Abstract
In this paper, we construct two goal-oriented a posteriori error estimates with finite element approximations in the enriched space for the reaction-diffusion equation with the nonlinear reaction term. The first error estimator is proved to be the rigorous global lower and upper bounds on the error in the quantity of interest, and the second one is computed simply and efficiently. We propose the corresponding goal-oriented adaptive finite element algorithms, and show the effectiveness and the similar performance of those methods with a series of numerical experiments. (c) 2022 Elsevier B.V. All rights reserved.
NSTL
Elsevier