# American Institute of Mathematical Sciences

October  2016, 9(5): 1393-1420. doi: 10.3934/dcdss.2016056

## A-posteriori error estimate for a heterogeneous multiscale approximation of advection-diffusion problems with large expected drift

 1 Department of Mathematics, KTH Royal Institute of Technology, SE-100 44 Stockholm 2 Institut für Numerische und Angewandte Mathematik, Westfälische Wilhelms-Universität Münster, Einsteinstr. 62, D-48149 Münster, Germany

Received  January 2015 Revised  March 2015 Published  October 2016

In this contribution we address a-posteriori error estimation in $L^\infty(L^2)$ for a heterogeneous multiscale finite element approximation of time-dependent advection-diffusion problems with rapidly oscillating coefficient functions and with a large expected drift. Based on the error estimate, we derive an algorithm for an adaptive mesh refinement. The estimate and the algorithm are validated in numerical experiments, showing applicability and good results even for heterogeneous microstructures.
Citation: Patrick Henning, Mario Ohlberger. A-posteriori error estimate for a heterogeneous multiscale approximation of advection-diffusion problems with large expected drift. Discrete and Continuous Dynamical Systems - S, 2016, 9 (5) : 1393-1420. doi: 10.3934/dcdss.2016056
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