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

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

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