The heterogeneous multiscale finite element method for advection-diffusion problems with rapidly oscillating coefficients and large expected drift

Patrick Henning; Mario Ohlberger

doi:10.3934/nhm.2010.5.711

Article Contents

2010, Volume 5, Issue 4: 711-744. Doi: 10.3934/nhm.2010.5.711

This issue Previous Article Classical solutions and feedback stabilization for the gas flow in a sequence of pipes Next Article Non-existence of positive stationary solutions for a class of semi-linear PDEs with random coefficients

The heterogeneous multiscale finite element method for advection-diffusion problems with rapidly oscillating coefficients and large expected drift

Patrick Henning^1, and
Mario Ohlberger^1,

1.
Institut für Numerische und Angewandte Mathematik, Fachbereich Mathematik und Informatik der Universität Münster, Einsteinstrasse 62, 48149 Münster

Received: March 2010

Revised: May 2010

Published: December 2010

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Abstract

This contribution is concerned with the formulation of a heterogeneous multiscale finite elements method (HMM) for solving linear advection-diffusion problems with rapidly oscillating coefficient functions and a large expected drift. We show that, in the case of periodic coefficient functions, this approach is equivalent to a discretization of the two-scale homogenized equation by means of a Discontinuous Galerkin Time Stepping Method with quadrature. We then derive an optimal order a-priori error estimate for this version of the HMM and finally provide numerical experiments to validate the method.

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Mathematics Subject Classification: Primary: 35K15, 35B45, 65N30.

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