Space–Time Adaption for Advection-Diffusion-Reaction Problems on Anisotropic Meshes

Abstract

We deal with the approximation of an unsteady advection-diffusion-reaction problem by means of space-time finite elements, continuous affine in space and piecewise constant in time. In particular, we are interested in the advection-dominated framework. To face the trade-off between computational cost and accuracy, we devise a space-time adaptive procedure where both the time step and the spatial grid are adapted throughout the simulation. Two are the key points involved: the derivation of an a posteriori error estimator where the contributions of the spatial and of the temporal discretization are split; a balance of these two contributions via a proper adaptive scheme. The main novelty of the paper is the interest for an anisotropic mesh adaption framework.