Abstract

We introduce and analyze a Residual Local Projection (RELP) adaptive finite element scheme for the advection-reaction-diffusion equation. This scheme is based on Franca et al. (2009) and combined with a residual a posteriori error estimator (see Verfurth, 1998). The a posteriori estimator is proved to be consistent, reliable, and efficient. More specifically, we proved global upper and local lower error estimates with constants, which are independent of the physical parameters and the mesh-size. Several numerical experiments illustrate the effectiveness of this method. (C) 2020 Elsevier B.V. All rights reserved.