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

Discrete and Continuous Dynamical Systems - Series S , Volume 9, Number 5, page 1393--1420 - 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.

Références BibTex

@Article{HO16b,
  author       = {Henning, P. and Ohlberger, M.},
  title        = {A-posteriori error estimate for a heterogeneous multiscale approximation of advection-diffusion problems with large expected drift},
  journal      = {Discrete and Continuous Dynamical Systems - Series S },
  number       = {5},
  volume       = {9},
  pages        = {1393--1420},
  month        = {october},
  year         = {2016},
  note         = {in press},
  keywords     = {Advection-diffusion, HMM, multiscale method, error estimation},
  doi          = {10.3934/dcdss.2016056},
  url          = \{/2016/HO16b},
}

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