Mesh adaptivity for the transport equation led by variational multiscale error estimators

Recently, we developed an explicit a posteriori error estimator especially suited for fluid dynamics problems solved with a stabilized method. The technology is based upon the theory that inspired stabilized methods, namely, the variational multiscale theory. The salient features of the formulation are that it can be readily implemented in existing codes, it is a very economical procedure, and it yields very accurate local error estimates uniformly from the diffusive to the advective regime. In this work, the variational multiscale error estimator is applied to develop adaptive strategies for the advection–diffusion‐reaction equation. The performance of L₁ and L₂ local error norms combined with three strategies to adapt the mesh is investigated. Emphasis is placed on flows with sharp boundary and interior layers but also attention is given to diffusion‐dominated flows. Computational results show that the method generates meshes with a smooth transition of the element size, which capture all the flow features. Copyright © 2011 John Wiley & Sons, Ltd.